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Showing papers in "IEEE Transactions on Image Processing in 2009"


Journal ArticleDOI

[...]

TL;DR: A fast algorithm is derived for the constrained TV-based image deblurring problem with box constraints by combining an acceleration of the well known dual approach to the denoising problem with a novel monotone version of a fast iterative shrinkage/thresholding algorithm (FISTA).
Abstract: This paper studies gradient-based schemes for image denoising and deblurring problems based on the discretized total variation (TV) minimization model with constraints. We derive a fast algorithm for the constrained TV-based image deburring problem. To achieve this task, we combine an acceleration of the well known dual approach to the denoising problem with a novel monotone version of a fast iterative shrinkage/thresholding algorithm (FISTA) we have recently introduced. The resulting gradient-based algorithm shares a remarkable simplicity together with a proven global rate of convergence which is significantly better than currently known gradient projections-based methods. Our results are applicable to both the anisotropic and isotropic discretized TV functionals. Initial numerical results demonstrate the viability and efficiency of the proposed algorithms on image deblurring problems with box constraints.

1,750 citations


Journal ArticleDOI

[...]

TL;DR: This paper shows how this denoising method is generalized to become a relatively simple super-resolution algorithm with no explicit motion estimation, and results show that the proposed method is very successful in providing super- resolution on general sequences.
Abstract: Super-resolution reconstruction proposes a fusion of several low-quality images into one higher quality result with better optical resolution. Classic super-resolution techniques strongly rely on the availability of accurate motion estimation for this fusion task. When the motion is estimated inaccurately, as often happens for nonglobal motion fields, annoying artifacts appear in the super-resolved outcome. Encouraged by recent developments on the video denoising problem, where state-of-the-art algorithms are formed with no explicit motion estimation, we seek a super-resolution algorithm of similar nature that will allow processing sequences with general motion patterns. In this paper, we base our solution on the Nonlocal-Means (NLM) algorithm. We show how this denoising method is generalized to become a relatively simple super-resolution algorithm with no explicit motion estimation. Results on several test movies show that the proposed method is very successful in providing super-resolution on general sequences.

807 citations


Journal ArticleDOI

[...]

TL;DR: The proposed features are robust to image rotation, less sensitive to histogram equalization and noise, and achieves the highest classification accuracy in various texture databases and image conditions.
Abstract: This paper proposes a novel approach to extract image features for texture classification. The proposed features are robust to image rotation, less sensitive to histogram equalization and noise. It comprises of two sets of features: dominant local binary patterns (DLBP) in a texture image and the supplementary features extracted by using the circularly symmetric Gabor filter responses. The dominant local binary pattern method makes use of the most frequently occurred patterns to capture descriptive textural information, while the Gabor-based features aim at supplying additional global textural information to the DLBP features. Through experiments, the proposed approach has been intensively evaluated by applying a large number of classification tests to histogram-equalized, randomly rotated and noise corrupted images in Outex, Brodatz, Meastex, and CUReT texture image databases. Our method has also been compared with six published texture features in the experiments. It is experimentally demonstrated that the proposed method achieves the highest classification accuracy in various texture databases and image conditions.

725 citations


Journal ArticleDOI

[...]

TL;DR: A general framework based on histogram equalization for image contrast enhancement, and a low-complexity algorithm for contrast enhancement is presented, and its performance is demonstrated against a recently proposed method.
Abstract: A general framework based on histogram equalization for image contrast enhancement is presented. In this framework, contrast enhancement is posed as an optimization problem that minimizes a cost function. Histogram equalization is an effective technique for contrast enhancement. However, a conventional histogram equalization (HE) usually results in excessive contrast enhancement, which in turn gives the processed image an unnatural look and creates visual artifacts. By introducing specifically designed penalty terms, the level of contrast enhancement can be adjusted; noise robustness, white/black stretching and mean-brightness preservation may easily be incorporated into the optimization. Analytic solutions for some of the important criteria are presented. Finally, a low-complexity algorithm for contrast enhancement is presented, and its performance is demonstrated against a recently proposed method.

681 citations


Journal ArticleDOI

[...]

TL;DR: Experimental results show that colorNames learned from real-world images significantly outperform color names learned from labeled color chips for both image retrieval and image annotation.
Abstract: Color names are required in real-world applications such as image retrieval and image annotation. Traditionally, they are learned from a collection of labeled color chips. These color chips are labeled with color names within a well-defined experimental setup by human test subjects. However, naming colors in real-world images differs significantly from this experimental setting. In this paper, we investigate how color names learned from color chips compare to color names learned from real-world images. To avoid hand labeling real-world images with color names, we use Google image to collect a data set. Due to the limitations of Google image, this data set contains a substantial quantity of wrongly labeled data. We propose several variants of the PLSA model to learn color names from this noisy data. Experimental results show that color names learned from real-world images significantly outperform color names learned from labeled color chips for both image retrieval and image annotation.

681 citations


Journal ArticleDOI

[...]

TL;DR: This work presents a perceptual-based no-reference objective image sharpness/blurriness metric by integrating the concept of just noticeable blur into a probability summation model that is able to predict with high accuracy the relative amount of blurriness in images with different content.
Abstract: This work presents a perceptual-based no-reference objective image sharpness/blurriness metric by integrating the concept of just noticeable blur into a probability summation model. Unlike existing objective no-reference image sharpness/blurriness metrics, the proposed metric is able to predict the relative amount of blurriness in images with different content. Results are provided to illustrate the performance of the proposed perceptual-based sharpness metric. These results show that the proposed sharpness metric correlates well with the perceived sharpness being able to predict with high accuracy the relative amount of blurriness in images with different content.

660 citations


Journal ArticleDOI

[...]

TL;DR: A framework for the joint design and optimization, from a set of training images, of the nonparametric dictionary and the sensing matrix is introduced and it is shown that this joint optimization outperforms both the use of random sensing matrices and those matrices that are optimized independently of the learning of the dictionary.
Abstract: Sparse signal representation, analysis, and sensing have received a lot of attention in recent years from the signal processing, optimization, and learning communities. On one hand, learning overcomplete dictionaries that facilitate a sparse representation of the data as a liner combination of a few atoms from such dictionary leads to state-of-the-art results in image and video restoration and classification. On the other hand, the framework of compressed sensing (CS) has shown that sparse signals can be recovered from far less samples than those required by the classical Shannon-Nyquist Theorem. The samples used in CS correspond to linear projections obtained by a sensing projection matrix. It has been shown that, for example, a nonadaptive random sampling matrix satisfies the fundamental theoretical requirements of CS, enjoying the additional benefit of universality. On the other hand, a projection sensing matrix that is optimally designed for a certain class of signals can further improve the reconstruction accuracy or further reduce the necessary number of samples. In this paper, we introduce a framework for the joint design and optimization, from a set of training images, of the nonparametric dictionary and the sensing matrix. We show that this joint optimization outperforms both the use of random sensing matrices and those matrices that are optimized independently of the learning of the dictionary. Particular cases of the proposed framework include the optimization of the sensing matrix for a given dictionary as well as the optimization of the dictionary for a predefined sensing environment. The presentation of the framework and its efficient numerical optimization is complemented with numerous examples on classical image datasets.

573 citations


Journal ArticleDOI

[...]

TL;DR: The proposed filter is an extension of the nonlocal means (NL means) algorithm introduced by Buades, which performs a weighted average of the values of similar pixels which depends on the noise distribution model.
Abstract: Image denoising is an important problem in image processing since noise may interfere with visual or automatic interpretation. This paper presents a new approach for image denoising in the case of a known uncorrelated noise model. The proposed filter is an extension of the nonlocal means (NL means) algorithm introduced by Buades, which performs a weighted average of the values of similar pixels. Pixel similarity is defined in NL means as the Euclidean distance between patches (rectangular windows centered on each two pixels). In this paper, a more general and statistically grounded similarity criterion is proposed which depends on the noise distribution model. The denoising process is expressed as a weighted maximum likelihood estimation problem where the weights are derived in a data-driven way. These weights can be iteratively refined based on both the similarity between noisy patches and the similarity of patches extracted from the previous estimate. We show that this iterative process noticeably improves the denoising performance, especially in the case of low signal-to-noise ratio images such as synthetic aperture radar (SAR) images. Numerical experiments illustrate that the technique can be successfully applied to the classical case of additive Gaussian noise but also to cases such as multiplicative speckle noise. The proposed denoising technique seems to improve on the state of the art performance in that latter case.

544 citations


Journal ArticleDOI

[...]

TL;DR: Results on real images demonstrate that the proposed adaptation of the nonlocal (NL)-means filter for speckle reduction in ultrasound (US) images is able to preserve accurately edges and structural details of the image.
Abstract: In image processing, restoration is expected to improve the qualitative inspection of the image and the performance of quantitative image analysis techniques. In this paper, an adaptation of the nonlocal (NL)-means filter is proposed for speckle reduction in ultrasound (US) images. Originally developed for additive white Gaussian noise, we propose to use a Bayesian framework to derive a NL-means filter adapted to a relevant ultrasound noise model. Quantitative results on synthetic data show the performances of the proposed method compared to well-established and state-of-the-art methods. Results on real images demonstrate that the proposed method is able to preserve accurately edges and structural details of the image.

490 citations


Journal ArticleDOI

[...]

TL;DR: A new measure of image similarity called the complex wavelet structural similarity (CW-SSIM) index is introduced and its applicability as a general purpose image similarity index is shown and it is demonstrated that it is computationally less expensive and robust to small rotations and translations.
Abstract: We introduce a new measure of image similarity called the complex wavelet structural similarity (CW-SSIM) index and show its applicability as a general purpose image similarity index. The key idea behind CW-SSIM is that certain image distortions lead to consistent phase changes in the local wavelet coefficients, and that a consistent phase shift of the coefficients does not change the structural content of the image. By conducting four case studies, we have demonstrated the superiority of the CW-SSIM index against other indices (e.g., Dice, Hausdorff distance) commonly used for assessing the similarity of a given pair of images. In addition, we show that the CW-SSIM index has a number of advantages. It is robust to small rotations and translations. It provides useful comparisons even without a preprocessing image registration step, which is essential for other indices. Moreover, it is computationally less expensive.

479 citations


Journal ArticleDOI

[...]

TL;DR: This paper introduces a novel framework for adaptive enhancement and spatiotemporal upscaling of videos containing complex activities without explicit need for accurate motion estimation based on multidimensional kernel regression, which significantly widens the applicability of super-resolution methods to a broad variety of video sequences containing complex motions.
Abstract: The need for precise (subpixel accuracy) motion estimates in conventional super-resolution has limited its applicability to only video sequences with relatively simple motions such as global translational or affine displacements. In this paper, we introduce a novel framework for adaptive enhancement and spatiotemporal upscaling of videos containing complex activities without explicit need for accurate motion estimation. Our approach is based on multidimensional kernel regression, where each pixel in the video sequence is approximated with a 3-D local (Taylor) series, capturing the essential local behavior of its spatiotemporal neighborhood. The coefficients of this series are estimated by solving a local weighted least-squares problem, where the weights are a function of the 3-D space-time orientation in the neighborhood. As this framework is fundamentally based upon the comparison of neighboring pixels in both space and time, it implicitly contains information about the local motion of the pixels across time, therefore rendering unnecessary an explicit computation of motions of modest size. The proposed approach not only significantly widens the applicability of super-resolution methods to a broad variety of video sequences containing complex motions, but also yields improved overall performance. Using several examples, we illustrate that the developed algorithm has super-resolution capabilities that provide improved optical resolution in the output, while being able to work on general input video with essentially arbitrary motion.

Journal ArticleDOI

[...]

Taiping Zhang1, Yuan Yan Tang1, Bin Fang1, Zhaowei Shang1, Xiaoyu Liu1 
TL;DR: Theoretical analysis and experimental results validate that gradient faces is an illumination insensitive measure, and robust to different illumination, including uncontrolled, natural lighting, and is also insensitive to image noise and object artifacts.
Abstract: In this correspondence, we propose a novel method to extract illumination insensitive features for face recognition under varying lighting called the gradient faces. Theoretical analysis shows gradient faces is an illumination insensitive measure, and robust to different illumination, including uncontrolled, natural lighting. In addition, gradient faces is derived from the image gradient domain such that it can discover underlying inherent structure of face images since the gradient domain explicitly considers the relationships between neighboring pixel points. Therefore, gradient faces has more discriminating power than the illumination insensitive measure extracted from the pixel domain. Recognition rates of 99.83% achieved on PIE database of 68 subjects, 98.96% achieved on Yale B of ten subjects, and 95.61% achieved on Outdoor database of 132 subjects under uncontrolled natural lighting conditions show that gradient faces is an effective method for face recognition under varying illumination. Furthermore, the experimental results on Yale database validate that gradient faces is also insensitive to image noise and object artifacts (such as facial expressions).

Journal ArticleDOI

[...]

TL;DR: This paper generalizes the above algorithm by offering several extensions: i) the atoms used are 3-D; ii) the dictionary is propagated from one frame to the next, reducing the number of required iterations; and iii) averaging is done on patches in both spatial and temporal neighboring locations.
Abstract: In this paper, we consider denoising of image sequences that are corrupted by zero-mean additive white Gaussian noise. Relative to single image denoising techniques, denoising of sequences aims to also utilize the temporal dimension. This assists in getting both faster algorithms and better output quality. This paper focuses on utilizing sparse and redundant representations for image sequence denoising. In the single image setting, the K-SVD algorithm is used to train a sparsifying dictionary for the corrupted image. This paper generalizes the above algorithm by offering several extensions: i) the atoms used are 3-D; ii) the dictionary is propagated from one frame to the next, reducing the number of required iterations; and iii) averaging is done on patches in both spatial and temporal neighboring locations. These modifications lead to substantial benefits in complexity and denoising performance, compared to simply running the single image algorithm sequentially. The algorithm's performance is experimentally compared to several state-of-the-art algorithms, demonstrating comparable or favorable results.

Journal ArticleDOI

[...]

TL;DR: This paper proposes a novel approach based on the shearlet transform: a multiscale directional transform with a greater ability to localize distributed discontinuities such as edges, which is useful to design simple and effective algorithms for the detection of corners and junctions.
Abstract: It is well known that the wavelet transform provides a very effective framework for analysis of multiscale edges. In this paper, we propose a novel approach based on the shearlet transform: a multiscale directional transform with a greater ability to localize distributed discontinuities such as edges. Indeed, unlike traditional wavelets, shearlets are theoretically optimal in representing images with edges and, in particular, have the ability to fully capture directional and other geometrical features. Numerical examples demonstrate that the shearlet approach is highly effective at detecting both the location and orientation of edges, and outperforms methods based on wavelets as well as other standard methods. Furthermore, the shearlet approach is useful to design simple and effective algorithms for the detection of corners and junctions.

Journal ArticleDOI

[...]

TL;DR: A novel face recognition method which exploits both global and local discriminative features, and which encodes the holistic facial information, such as facial contour, is proposed.
Abstract: In the literature of psychophysics and neurophysiology, many studies have shown that both global and local features are crucial for face representation and recognition. This paper proposes a novel face recognition method which exploits both global and local discriminative features. In this method, global features are extracted from the whole face images by keeping the low-frequency coefficients of Fourier transform, which we believe encodes the holistic facial information, such as facial contour. For local feature extraction, Gabor wavelets are exploited considering their biological relevance. After that, Fisher's linear discriminant (FLD) is separately applied to the global Fourier features and each local patch of Gabor features. Thus, multiple FLD classifiers are obtained, each embodying different facial evidences for face recognition. Finally, all these classifiers are combined to form a hierarchical ensemble classifier. We evaluate the proposed method using two large-scale face databases: FERET and FRGC version 2.0. Experiments show that the results of our method are impressively better than the best known results with the same evaluation protocol.

Journal ArticleDOI

[...]

TL;DR: This paper proposes K-LLD: a patch-based, locally adaptive denoising method based on clustering the given noisy image into regions of similar geometric structure and introduces a novel mechanism for optimally choosing the local patch size for each cluster using Stein's unbiased risk estimators.
Abstract: In this paper, we propose K-LLD: a patch-based, locally adaptive denoising method based on clustering the given noisy image into regions of similar geometric structure. In order to effectively perform such clustering, we employ as features the local weight functions derived from our earlier work on steering kernel regression . These weights are exceedingly informative and robust in conveying reliable local structural information about the image even in the presence of significant amounts of noise. Next, we model each region (or cluster)-which may not be spatially contiguous-by ldquolearningrdquo a best basis describing the patches within that cluster using principal components analysis. This learned basis (or ldquodictionaryrdquo) is then employed to optimally estimate the underlying pixel values using a kernel regression framework. An iterated version of the proposed algorithm is also presented which leads to further performance enhancements. We also introduce a novel mechanism for optimally choosing the local patch size for each cluster using Stein's unbiased risk estimator (SURE). We illustrate the overall algorithm's capabilities with several examples. These indicate that the proposed method appears to be competitive with some of the most recently published state of the art denoising methods.

Journal ArticleDOI

[...]

TL;DR: The achieved experimental results from the proposed system using contactless palm dorsal-hand vein images are promising and suggest more user friendly alternative for user identification.
Abstract: This paper presents a new approach to authenticate individuals using triangulation of hand vein images and simultaneous extraction of knuckle shape information. The proposed method is fully automated and employs palm dorsal hand vein images acquired from the low-cost, near infrared, contactless imaging. The knuckle tips are used as key points for the image normalization and extraction of region of interest. The matching scores are generated in two parallel stages: (i) hierarchical matching score from the four topologies of triangulation in the binarized vein structures and (ii) from the geometrical features consisting of knuckle point perimeter distances in the acquired images. The weighted score level combination from these two matching scores are used to authenticate the individuals. The achieved experimental results from the proposed system using contactless palm dorsal-hand vein images are promising (equal error rate of 1.14%) and suggest more user friendly alternative for user identification.

Journal ArticleDOI

[...]

TL;DR: This paper proposes a fast background subtraction scheme using independent component analysis (ICA) and aims at indoor surveillance for possible applications in home-care and health-care monitoring, where moving and motionless persons must be reliably detected.
Abstract: In video surveillance, detection of moving objects from an image sequence is very important for target tracking, activity recognition, and behavior understanding. Background subtraction is a very popular approach for foreground segmentation in a still scene image. In order to compensate for illumination changes, a background model updating process is generally adopted, and leads to extra computation time. In this paper, we propose a fast background subtraction scheme using independent component analysis (ICA) and, particularly, aims at indoor surveillance for possible applications in home-care and health-care monitoring, where moving and motionless persons must be reliably detected. The proposed method is as computationally fast as the simple image difference method, and yet is highly tolerable to changes in room lighting. The proposed background subtraction scheme involves two stages, one for training and the other for detection. In the training stage, an ICA model that directly measures the statistical independency based on the estimations of joint and marginal probability density functions from relative frequency distributions is first proposed. The proposed ICA model can well separate two highly-correlated images. In the detection stage, the trained de-mixing vector is used to separate the foreground in a scene image with respect to the reference background image. Two sets of indoor examples that involve switching on/off room lights and opening/closing a door are demonstrated in the experiments. The performance of the proposed ICA model for background subtraction is also compared with that of the well-known FastICA algorithm.

Journal ArticleDOI

[...]

TL;DR: The prior knowledge extracted from the psychological experiments can be combined with an automatic method to further improve classification accuracy, and the proposed method achieves higher performance than some other methods, and is even more accurate than human observers.
Abstract: Gender is an important cue in social activities. In this correspondence, we present a study and analysis of gender classification based on human gait. Psychological experiments were carried out. These experiments showed that humans can recognize gender based on gait information, and that contributions of different body components vary. The prior knowledge extracted from the psychological experiments can be combined with an automatic method to further improve classification accuracy. The proposed method which combines human knowledge achieves higher performance than some other methods, and is even more accurate than human observers. We also present a numerical analysis of the contributions of different human components, which shows that head and hair, back, chest and thigh are more discriminative than other components. We also did challenging cross-race experiments that used Asian gait data to classify the gender of Europeans, and vice versa. Encouraging results were obtained. All the above prove that gait-based gender classification is feasible in controlled environments. In real applications, it still suffers from many difficulties, such as view variation, clothing and shoes changes, or carrying objects. We analyze the difficulties and suggest some possible solutions.

Journal ArticleDOI

[...]

TL;DR: A novel framework for IQA to mimic the human visual system (HVS) by incorporating the merits from multiscale geometric analysis (MGA), contrast sensitivity function (CSF), and the Weber's law of just noticeable difference (JND) is developed.
Abstract: Reduced-reference (RR) image quality assessment (IQA) has been recognized as an effective and efficient way to predict the visual quality of distorted images. The current standard is the wavelet-domain natural image statistics model (WNISM), which applies the Kullback-Leibler divergence between the marginal distributions of wavelet coefficients of the reference and distorted images to measure the image distortion. However, WNISM fails to consider the statistical correlations of wavelet coefficients in different subbands and the visual response characteristics of the mammalian cortical simple cells. In addition, wavelet transforms are optimal greedy approximations to extract singularity structures, so they fail to explicitly extract the image geometric information, e.g., lines and curves. Finally, wavelet coefficients are dense for smooth image edge contours. In this paper, to target the aforementioned problems in IQA, we develop a novel framework for IQA to mimic the human visual system (HVS) by incorporating the merits from multiscale geometric analysis (MGA), contrast sensitivity function (CSF), and the Weber's law of just noticeable difference (JND). In the proposed framework, MGA is utilized to decompose images and then extract features to mimic the multichannel structure of HVS. Additionally, MGA offers a series of transforms including wavelet, curvelet, bandelet, contourlet, wavelet-based contourlet transform (WBCT), and hybrid wavelets and directional filter banks (HWD), and different transforms capture different types of image geometric information. CSF is applied to weight coefficients obtained by MGA to simulate the appearance of images to observers by taking into account many of the nonlinearities inherent in HVS. JND is finally introduced to produce a noticeable variation in sensory experience. Thorough empirical studies are carried out upon the LIVE database against subjective mean opinion score (MOS) and demonstrate that 1) the proposed framework has good consistency with subjective perception values and the objective assessment results can well reflect the visual quality of images, 2) different transforms in MGA under the new framework perform better than the standard WNISM and some of them even perform better than the standard full-reference IQA model, i.e., the mean structural similarity index, and 3) HWD performs best among all transforms in MGA under the framework.

Journal ArticleDOI

[...]

TL;DR: This work describes an alternative approach that minimizes a generalized TV functional, including both lscr2-TV and lscR1-TV as special cases, and is capable of solving more general inverse problems than denoising (e.g., deconvolution).
Abstract: Replacing the lscr2 data fidelity term of the standard total variation (TV) functional with an lscr1 data fidelity term has been found to offer a number of theoretical and practical benefits. Efficient algorithms for minimizing this lscr1-TV functional have only recently begun to be developed, the fastest of which exploit graph representations, and are restricted to the denoising problem. We describe an alternative approach that minimizes a generalized TV functional, including both lscr2-TV and lscr1-TV as special cases, and is capable of solving more general inverse problems than denoising (e.g., deconvolution). This algorithm is competitive with the graph-based methods in the denoising case, and is the fastest algorithm of which we are aware for general inverse problems involving a nontrivial forward linear operator.

Journal ArticleDOI

[...]

TL;DR: An in-depth analysis of a variation of the nonlocal means (NLM) image denoising algorithm that uses principal component analysis (PCA) to achieve a higher accuracy while reducing computational load.
Abstract: We present an in-depth analysis of a variation of the nonlocal means (NLM) image denoising algorithm that uses principal component analysis (PCA) to achieve a higher accuracy while reducing computational load. Image neighborhood vectors are first projected onto a lower dimensional subspace using PCA. The dimensionality of this subspace is chosen automatically using parallel analysis. Consequently, neighborhood similarity weights for denoising are computed using distances in this subspace rather than the full space. The resulting algorithm is referred to as principal neighborhood dictionary (PND) nonlocal means. We investigate PND's accuracy as a function of the dimensionality of the projection subspace and demonstrate that denoising accuracy peaks at a relatively low number of dimensions. The accuracy of NLM and PND are also examined with respect to the choice of image neighborhood and search window sizes. Finally, we present a quantitative and qualitative comparison of PND versus NLM and another image neighborhood PCA-based state-of-the-art image denoising algorithm.

Journal ArticleDOI

[...]

TL;DR: Novel algorithms for total variation (TV) based blind deconvolution and parameter estimation utilizing a variational framework using a hierarchical Bayesian model to provide higher restoration performance than non-TV-based methods without any assumptions about the unknown hyperparameters.
Abstract: In this paper, we present novel algorithms for total variation (TV) based blind deconvolution and parameter estimation utilizing a variational framework. Using a hierarchical Bayesian model, the unknown image, blur, and hyperparameters for the image, blur, and noise priors are estimated simultaneously. A variational inference approach is utilized so that approximations of the posterior distributions of the unknowns are obtained, thus providing a measure of the uncertainty of the estimates. Experimental results demonstrate that the proposed approaches provide higher restoration performance than non-TV-based methods without any assumptions about the unknown hyperparameters.

Journal ArticleDOI

[...]

TL;DR: The results suggest that using sparse-domain regularization may be tractable in many deconvolution applications with Poisson noise such as astronomy and microscopy.
Abstract: We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transforms. Our key contributions are as follows. First, we handle the Poisson noise properly by using the Anscombe variance stabilizing transform leading to a nonlinear degradation equation with additive Gaussian noise. Second, the deconvolution problem is formulated as the minimization of a convex functional with a data-fidelity term reflecting the noise properties, and a nonsmooth sparsity-promoting penalty over the image representation coefficients (e.g., lscr1 -norm). An additional term is also included in the functional to ensure positivity of the restored image. Third, a fast iterative forward-backward splitting algorithm is proposed to solve the minimization problem. We derive existence and uniqueness conditions of the solution, and establish convergence of the iterative algorithm. Finally, a GCV-based model selection procedure is proposed to objectively select the regularization parameter. Experimental results are carried out to show the striking benefits gained from taking into account the Poisson statistics of the noise. These results also suggest that using sparse-domain regularization may be tractable in many deconvolution applications with Poisson noise such as astronomy and microscopy.

Journal ArticleDOI

[...]

TL;DR: It is shown that it is possible to obtain much better estimates from aShearlet representation by constraining the residual coefficients using a projected adaptive total variation scheme in the shearlet domain.
Abstract: We propose a shearlet formulation of the total variation (TV) method for denoising images. Shearlets have been mathematically proven to represent distributed discontinuities such as edges better than traditional wavelets and are a suitable tool for edge characterization. Common approaches in combining wavelet-like representations such as curvelets with TV or diffusion methods aim at reducing Gibbs-type artifacts after obtaining a nearly optimal estimate. We show that it is possible to obtain much better estimates from a shearlet representation by constraining the residual coefficients using a projected adaptive total variation scheme in the shearlet domain. We also analyze the performance of a shearlet-based diffusion method. Numerical examples demonstrate that these schemes are highly effective at denoising complex images and outperform a related method based on the use of the curvelet transform. Furthermore, the shearlet-TV scheme requires far fewer iterations than similar competitors.

Journal ArticleDOI

[...]

TL;DR: A complexified version of the Riesz transform which has the remarkable property of mapping a real-valued wavelet basis of L2(R2) into a complex one is considered, which yields a representation where each wavelet index is associated with a local orientation, an amplitude and a phase.
Abstract: The monogenic signal is the natural 2D counterpart of the 1D analytic signal. We propose to transpose the concept to the wavelet domain by considering a complexified version of the Riesz transform which has the remarkable property of mapping a real-valued (primary) wavelet basis of L2(R2) into a complex one. The Riesz operator is also steerable in the sense that it give access to the Hilbert transform of the signal along any orientation. Having set those foundations, we specify a primary polyharmonic spline wavelet basis of L2(R2) that involves a single Mexican-hat-like mother wavelet (Laplacian of a B-spline). The important point is that our primary wavelets are quasi-isotropic: they behave like multiscale versions of the fractional Laplace operator from which they are derived, which ensures steerability. We propose to pair these real-valued basis functions with their complex Riesz counterparts to specify a multiresolution monogenic signal analysis. This yields a representation where each wavelet index is associated with a local orientation, an amplitude and a phase. We give a corresponding wavelet-domain method for estimating the underlying instantaneous frequency. We also provide a mechanism for improving the shift and rotation-invariance of the wavelet decomposition and show how to implement the transform efficiently using perfect-reconstruction filterbanks. We illustrate the specific feature-extraction capabilities of the representation and present novel examples of wavelet-domain processing; in particular, a robust, tensor-based analysis of directional image patterns, the demodulation of interferograms, and the reconstruction of digital holograms.

Journal ArticleDOI

[...]

TL;DR: A new filtering method to remove Rician noise from magnetic resonance images is presented that relies on a robust estimation of the standard deviation of the noise and combines local linear minimum mean square error filters and partial differential equations for MRI, as the speckle reducing anisotropic diffusion did for ultrasound images.
Abstract: A new filtering method to remove Rician noise from magnetic resonance images is presented. This filter relies on a robust estimation of the standard deviation of the noise and combines local linear minimum mean square error filters and partial differential equations for MRI, as the speckle reducing anisotropic diffusion did for ultrasound images. The parameters of the filter are automatically chosen from the estimated noise. This property improves the convergence rate of the diffusion while preserving contours, leading to more robust and intuitive filtering. The partial derivative equation of the filter is extended to a new matrix diffusion filter which allows a coherent diffusion based on the local structure of the image and on the corresponding oriented local standard deviations. This new filter combines volumetric, planar, and linear components of the local image structure. The numerical scheme is explained and visual and quantitative results on simulated and real data sets are presented. In the experiments, the new filter leads to the best results.

Journal ArticleDOI

[...]

TL;DR: This paper shows that this formulation of the active-contour energy functional allows us to compute the solution as a restriction of the variational problem on the space spanned by the B-splines, and shows that each step of this minimization may be expressed through a convolution operation.
Abstract: In the field of image segmentation, most level-set-based active-contour approaches take advantage of a discrete representation of the associated implicit function. We present in this paper a different formulation where the implicit function is modeled as a continuous parametric function expressed on a B-spline basis. Starting from the active-contour energy functional, we show that this formulation allows us to compute the solution as a restriction of the variational problem on the space spanned by the B-splines. As a consequence, the minimization of the functional is directly obtained in terms of the B-spline coefficients. We also show that each step of this minimization may be expressed through a convolution operation. Because the B-spline functions are separable, this convolution may in turn be performed as a sequence of simple 1-D convolutions, which yields an efficient algorithm. As a further consequence, each step of the level-set evolution may be interpreted as a filtering operation with a B-spline kernel. Such filtering induces an intrinsic smoothing in the algorithm, which can be controlled explicitly via the degree and the scale of the chosen B-spline kernel. We illustrate the behavior of this approach on simulated as well as experimental images from various fields.

Journal ArticleDOI

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TL;DR: A novel combination of this soft edge smoothness prior and the alpha matting technique for color image SR, by adaptively normalizing image edges according to their alpha-channel description leads to the adaptive SoftCuts algorithm, which represents a unified treatment of edges with different contrasts and scales.
Abstract: Designing effective image priors is of great interest to image super-resolution (SR), which is a severely under-determined problem. An edge smoothness prior is favored since it is able to suppress the jagged edge artifact effectively. However, for soft image edges with gradual intensity transitions, it is generally difficult to obtain analytical forms for evaluating their smoothness. This paper characterizes soft edge smoothness based on a novel SoftCuts metric by generalizing the Geocuts method . The proposed soft edge smoothness measure can approximate the average length of all level lines in an intensity image. Thus, the total length of all level lines can be minimized effectively by integrating this new form of prior. In addition, this paper presents a novel combination of this soft edge smoothness prior and the alpha matting technique for color image SR, by adaptively normalizing image edges according to their alpha-channel description. This leads to the adaptive SoftCuts algorithm, which represents a unified treatment of edges with different contrasts and scales. Experimental results are presented which demonstrate the effectiveness of the proposed method.

Journal ArticleDOI

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TL;DR: A new unsupervised color image segmentation algorithm is proposed, which exploits the information obtained from detecting edges in color images in the CIE L*a*b* color space to identify some initial portion of the input image content.
Abstract: Image segmentation is a fundamental task in many computer vision applications. In this paper, we propose a new unsupervised color image segmentation algorithm, which exploits the information obtained from detecting edges in color images in the CIE L*a*b* color space. To this effect, by using a color gradient detection technique, pixels without edges are clustered and labeled individually to identify some initial portion of the input image content. Elements that contain higher gradient densities are included by the dynamic generation of clusters as the algorithm progresses. Texture modeling is performed by color quantization and local entropy computation of the quantized image. The obtained texture and color information along with a region growth map consisting of all fully grown regions are used to perform a unique multiresolution merging procedure to blend regions with similar characteristics. Experimental results obtained in comparison to published segmentation techniques demonstrate the performance advantages of the proposed method.