scispace - formally typeset
Proceedings ArticleDOI

Poisson noise removal from images using the fast discrete Curvelet transform

17 Mar 2011-pp 1-5
TL;DR: The results show that the VST combined with the FDCT is a promising candidate for Poisson denoising, and a simple approach to achieve this is presented.

...read more

Abstract: We propose a strategy to combine the variance stabilizing transform (VST), used for Poisson image denoising, with the fast discrete Curvelet transform (FDCT). The VST transforms the Poisson image to approximately Gaussian distributed, and the subsequent denoising can be performed in the Gaussian domain. However, the performance of the VST degrades when the original image intensity is very low. On the other hand, the FDCT can sparsely represent the intrinsic features of images having discontinuities along smooth curves. Therefore, it is suitable for denoising applications. Combining the VST with the FDCT leads to good Poisson image denoising algorithms, even for low intensity images. We present a simple approach to achieve this and demonstrate some simulation results. The results show that the VST combined with the FDCT is a promising candidate for Poisson denoising.

...read more

Citations
More filters

Journal ArticleDOI
Sandeep Palakkal1, K.M.M. Prabhu1Institutions (1)
01 Sep 2012-Signal Processing
TL;DR: The results demonstrate that the MS-VST combined with FDCT and WA are promising candidates for Poisson denoising, and a simple strategy to achieve this without increasing the computational complexity is proposed.

...read more

Abstract: In this paper, we propose a strategy to combine fast discrete curvelet transform (FDCT) and wave atom (WA) with multiscale variance stabilizing transform (MS-VST); our objective is to develop algorithms for Poisson noise removal from images. Applying variance stabilizing transform (VST) on a Poisson noisy image results in a nearly Gaussian distributed image. The noise removal can be subsequently done assuming a Gaussian noise model. MS-VST has been recently proposed in the literature (i) to improve the denoising performance of Anscombe's VST at low intensity regions of the image and (ii) to facilitate the use of multiscale-multidirectional transforms like the curvelet transform for Poisson image denoising. Since the MS-VST has been implemented in the space-domain, it is not clear how it can be extended to FDCT and WA, which are incidentally implemented in the frequency-domain. We propose a simple strategy to achieve this without increasing the computational complexity. We also extend our approach to handle the recently developed mirror-extended versions of FDCT and WA. We have carried out simulations to validate the performance of the proposed approach. The results demonstrate that the MS-VST combined with FDCT and WA are promising candidates for Poisson denoising.

...read more

19 citations


Book ChapterDOI
01 Jan 2015-
TL;DR: The recently developed denoising approach called the Poisson Unbiased Risk Estimation-Linear Expansion of Thresholds (PURE-LET) is implemented to improve the peak signal to noise ratio (PSNR) further and successfully removes Poisson noise better than the traditional mathematical transforms.

...read more

Abstract: We present an experimental work on the denoising of mammogram with Poisson noise. Reviewing the literature, it is found that the denoising performance of the multiresolution tools like wavelet, contourlet and curvelet implemented on mammogram with Poisson noise is unique. The first part of the investigation deals with the confirmation of this exceptional performance with our result. The later half implements the recently developed denoising approach called the Poisson Unbiased Risk Estimation-Linear Expansion of Thresholds (PURE-LET) to the Poisson noise corrupted mammogram with an objective to improve the peak signal to noise ratio (PSNR) further. The PURE-LET successfully removes Poisson noise better than the traditional mathematical transforms already mentioned. The computation time and PSNR are also evaluated in the perspective of the cycle spinning technique. This validates the applicability and efficiency of the novel denoising strategy in the field of digital mammography.

...read more

2 citations


Journal Article
TL;DR: Two technique which combines Multi-Scale Variance Stabilizing Transform, Fast Discrete Curvelet Transform with Thresholding and MS-VST, FDCT with Null Hypothesis testing for effectively removing the Poisson Noise from the medical images are proposed.

...read more

Abstract: Medical images have always been an important factor in diagnosis of disease. Poisson Noise in those images has always been a problem with the image clarity. We propose two technique which combines Multi-Scale Variance Stabilizing Transform (MS-VST), Fast Discrete Curvelet Transform (FDCT) with Thresholding and MS-VST, FDCT with Null Hypothesis testing for effectively removing the Poisson Noise from the medical images. The effectiveness of using these techniques has been analyzed using Peak Signal to Noise Ratio and Universal Image Quality Index.

...read more

2 citations


Cites background or methods from "Poisson noise removal from images u..."

  • ...FDCT [1]-[2] is a second generation curvelet transform which is a multi resolution method....

    [...]

  • ...MS-VST [1] stabilizes the variance in Poisson Noise affected images and Gaussianize it to an extent....

    [...]


01 Jan 2013-
TL;DR: Two methods of removing poisson noise from images using a bilateral filter and by Fast discrete Curvelet Transform (FDCT), which show that FDCT is more efficient for preserving image features, while bilateral filter is much faster and simple to implement.

...read more

Abstract: We analyse two methods of removing poisson noise from images using a bilateral filter and by Fast discrete Curvelet Transform (FDCT). The Variance stabilizing transform (VST) is the main feature of the noise removal as it converts the Poisson distribution to the Gaussian domain, which makes the noise removal process relatively simple. Once the Gaussian distribution is obtained, the bilateral filter (BF) can be used for removing noise. We can also use the FDCT instead of bilateral filter, as it is capable of sparse representation of image intrinsic features. We implement both the methods separately, compare them and demonstrate simulations for monitoring their effectiveness in poisson noise removal. The results show that FDCT is more efficient for preserving image features, while bilateral filter is much faster and simple to implement.

...read more

1 citations


Cites methods from "Poisson noise removal from images u..."

  • ...1 Combining MS-VST with FDCT Combination of MS-VST with FDCT [6] begins with the design of lowpass filter banks which depends on the number of scales used....

    [...]


Journal ArticleDOI
TL;DR: A novel approach for accomplishing Poisson noise removal in biomedical images by multiresolution representation where Fast Discrete Curvelet Transform is integrated with Rudin–Osher–Fatemi (ROF) model based on VST.

...read more

Abstract: This paper introduces a novel approach for accomplishing Poisson noise removal in biomedical images by multiresolution representation. Methods of denoising are described based on three classical methods: (1) Fast Discrete Curvelet Transform (FDCT) with simple soft thresholding, (2) Variance Stabilizing Transform (VST) combined with FDCT where hypothesis tests are made to detect the significant coefficients and (3) The proposed method where the FDCT is integrated with Rudin–Osher–Fatemi (ROF) model. Much of the literature has focused on developing algorithms for the removal of Gaussian noise where the estimation is often done by finding a Curvelet and by thresholding the noisy coefficients. However not much has been done to remove Poisson noise in biomedical images. But in most of the medical images, the recorded data are not modeled by Gaussian noise but is the realization of Poisson process. Hence, in this work, FDCT integrated with ROF model based on VST is proposed. The VST is applied so that the transformed data are homoscedastic and Gaussian. A classical hypothesis testing framework is used to detect the significant coefficients and an iterative scheme is used to reconstruct the final estimate. A central difference total variation term in the discrete ROF model is used. The model is experimented on a large number of clinical images like Computed Tomography (CT) images, X-Ray images, Positron Emission Tomography (PET) images and Single Photon Emission Computed Tomography (SPECT) images and the performances are evaluated in terms of Peak Signal to Noise Ratio (PSNR) and the Universal Quality Index (UQI). The results are compared with those obtained by the other two existing algorithms proposed in the literature. Numerical results show that the proposed algorithm obtains higher PSNR and UQI than the other two methods.

...read more

1 citations


References
More filters

Journal ArticleDOI
Abstract: SUMMARY The common approach to the multiplicity problem calls for controlling the familywise error rate (FWER). This approach, though, has faults, and we point out a few. A different approach to problems of multiple significance testing is presented. It calls for controlling the expected proportion of falsely rejected hypotheses -the false discovery rate. This error rate is equivalent to the FWER when all hypotheses are true but is smaller otherwise. Therefore, in problems where the control of the false discovery rate rather than that of the FWER is desired, there is potential for a gain in power. A simple sequential Bonferronitype procedure is proved to control the false discovery rate for independent test statistics, and a simulation study shows that the gain in power is substantial. The use of the new procedure and the appropriateness of the criterion are illustrated with examples.

...read more

71,936 citations


"Poisson noise removal from images u..." refers methods in this paper

  • ...Then we perform hard thresholding to detect the significant FDCT coefficients for a prespecified false detection rate (FDR) [10]....

    [...]

  • ...A few important specifications of our experiments are: five scales and {8, 16, 16, 32, 32} directions (from coarse to fine) for the MSMD transforms except the first generation curvelet, for which four scales are used; the FDCT implementation based on frequency wrapping; images of size 256×256 and intensity in the range [0.9, 20]; and FDR = 10−3 and number of iterations in HSD = 5 [3]....

    [...]


Journal ArticleDOI
TL;DR: This paper describes two digital implementations of a new mathematical transform, namely, the second generation curvelet transform in two and three dimensions, based on unequally spaced fast Fourier transforms, while the second is based on the wrapping of specially selected Fourier samples.

...read more

Abstract: This paper describes two digital implementations of a new mathematical transform, namely, the second generation curvelet transform in two and three dimensions. The first digital transformation is based on unequally spaced fast Fourier transforms, while the second is based on the wrapping of specially selected Fourier samples. The two implementations essentially differ by the choice of spatial grid used to translate curvelets at each scale and angle. Both digital transformations return a table of digital curvelet coefficients indexed by a scale parameter, an orientation parameter, and a spatial location parameter. And both implementations are fast in the sense that they run in O(n^2 log n) flops for n by n Cartesian arrays; in addition, they are also invertible, with rapid inversion algorithms of about the same complexity. Our digital transformations improve upon earlier implementations—based upon the first generation of curvelets—in the sense that they are conceptually simpler, faster, and far less redundant. The software CurveLab, which implements both transforms presented in this paper, is available at http://www.curvelet.org.

...read more

2,446 citations


"Poisson noise removal from images u..." refers methods in this paper

  • ...Two separate digital implementation of the second generation curvelets were proposed in [7]....

    [...]

  • ...In this paper, we propose a strategy to combine the MS-VST with the second generation curvelet transform, specifically the fast discrete curvelet transform (FDCT) [7]....

    [...]

  • ...Similarly, when compared to the NSCT, the FDCT is less redundant and has more frequency resolution and better directionality properties [7]....

    [...]


Journal ArticleDOI
A.L. da Cunha1, Jianping Zhou1, Minh N. Do1Institutions (1)
TL;DR: This paper proposes a design framework based on the mapping approach, that allows for a fast implementation based on a lifting or ladder structure, and only uses one-dimensional filtering in some cases.

...read more

Abstract: In this paper, we develop the nonsubsampled contourlet transform (NSCT) and study its applications. The construction proposed in this paper is based on a nonsubsampled pyramid structure and nonsubsampled directional filter banks. The result is a flexible multiscale, multidirection, and shift-invariant image decomposition that can be efficiently implemented via the a trous algorithm. At the core of the proposed scheme is the nonseparable two-channel nonsubsampled filter bank (NSFB). We exploit the less stringent design condition of the NSFB to design filters that lead to a NSCT with better frequency selectivity and regularity when compared to the contourlet transform. We propose a design framework based on the mapping approach, that allows for a fast implementation based on a lifting or ladder structure, and only uses one-dimensional filtering in some cases. In addition, our design ensures that the corresponding frame elements are regular, symmetric, and the frame is close to a tight one. We assess the performance of the NSCT in image denoising and enhancement applications. In both applications the NSCT compares favorably to other existing methods in the literature

...read more

1,730 citations


4


"Poisson noise removal from images u..." refers background or methods in this paper

  • ...In fact, the NMISE is very close to that of the NSCT and better than that of the SNSCT....

    [...]

  • ...L Donoho, and the NSCT Toolbox prepared by A. L. Cunha, for conducting the simulations given in this paper....

    [...]

  • ...4d), which is a semi nonsubsampled version of the NSCT [5], [6]....

    [...]

  • ...The MS-VST+NSCT (Fig....

    [...]

  • ...Recently, we have proposed [5] an MS-VST Poisson image denoising algorithm, based on the nonsubsampled contourlet transform (NSCT) [6]....

    [...]


01 Jan 2000-
TL;DR: The basic issues of efficient m-term approximation, the construction of efficient adaptive representation, theConstruction of the curvelet frame, and a crude analysis of the performance of curvelet schemes are explained.

...read more

Abstract: : It is widely believed that to efficiently represent an otherwise smooth object with discontinuities along edges, one must use an adaptive representation that in some sense 'tracks' the shape of the discontinuity set. This folk-belief - some would say folk-theorem - is incorrect. At the very least, the possible quantitative advantage of such adaptation is vastly smaller than commonly believed. We have recently constructed a tight frame of curvelets which provides stable, efficient, and near-optimal representation of otherwise smooth objects having discontinuities along smooth curves. By applying naive thresholding to the curvelet transform of such an object, one can form m-term approximations with rate of L(sup 2) approximation rivaling the rate obtainable by complex adaptive schemes which attempt to track' the discontinuity set. In this article we explain the basic issues of efficient m-term approximation, the construction of efficient adaptive representation, the construction of the curvelet frame, and a crude analysis of the performance of curvelet schemes.

...read more

1,610 citations


"Poisson noise removal from images u..." refers background or methods in this paper

  • ...The curvelet transforms, first generation [4] as well as...

    [...]

  • ...In [3], MS-VSTs were developed for the wavelet, ridgelet and first generation curvelet transforms [4], and the curvelet was shown to yield the best performance....

    [...]


Journal ArticleDOI
Emmanuel J. Candès1, David L. Donoho2Institutions (2)
TL;DR: This paper introduces new tight frames of curvelets to address the problem of finding optimally sparse representations of objects with discontinuities along piecewise C2 edges.

...read more

Abstract: This paper introduces new tight frames of curvelets to address the problem of finding optimally sparse representations of objects with discontinuities along piecewise C 2 edges. Conceptually, the curvelet transform is a multiscale pyramid with many directions and positions at each length scale, and needle-shaped elements at fine scales. These elements have many useful geometric multiscale features that set them apart from classical multiscale representations such as wavelets. For instance, curvelets obey a parabolic scaling relation which says that at scale 2 -j , each element has an envelope that is aligned along a ridge of length 2 -j/2 and width 2 -j . We prove that curvelets provide an essentially optimal representation of typical objects f that are C 2 except for discontinuities along piecewise C 2 curves. Such representations are nearly as sparse as if f were not singular and turn out to be far more sparse than the wavelet decomposition of the object. For instance, the n-term partial reconstruction f C n obtained by selecting the n largest terms in the curvelet series obeys ∥f - f C n ∥ 2 L2 ≤ C . n -2 . (log n) 3 , n → ∞. This rate of convergence holds uniformly over a class of functions that are C 2 except for discontinuities along piecewise C 2 curves and is essentially optimal. In comparison, the squared error of n-term wavelet approximations only converges as n -1 as n → ∞, which is considerably worse than the optimal behavior.

...read more

1,494 citations


"Poisson noise removal from images u..." refers background in this paper

  • ...second generation [8], provide a near-optimal sparse representation for images having discontinuities along C(2) (twice differentiable) curves....

    [...]


Performance
Metrics
No. of citations received by the Paper in previous years
YearCitations
20151
20143
20131
20122