We present a nonparametric algorithm for finding localized energy solutions from limited data. The problem we address is underdetermined, and no prior knowledge of the shape of the region on which the solution is nonzero is assumed. Termed the FOcal Underdetermined System Solver (FOCUSS), the algorithm has two integral parts: a low-resolution initial estimate of the real signal and the iteration process that refines the initial estimate to the final localized energy solution. The iterations are based on weighted norm minimization of the dependent variable with the weights being a function of the preceding iterative solutions. The algorithm is presented as a general estimation tool usable across different applications. A detailed analysis laying the theoretical foundation for the algorithm is given and includes proofs of global and local convergence and a derivation of the rate of convergence. A view of the algorithm as a novel optimization method which combines desirable characteristics of both classical optimization and learning-based algorithms is provided. Mathematical results on conditions for uniqueness of sparse solutions are also given. Applications of the algorithm are illustrated on problems in direction-of-arrival (DOA) estimation and neuromagnetic imaging.

Sparse signal reconstruction from limited data using FOCUSS: a re-weighted minimum norm algorithm

Image enhancement plays an important role in image processing and analysis. Among various enhancement algorithms, Retinex-based algorithms can efficiently enhance details and have been widely adopted. Since Retinex-based algorithms regard illumination removal as a default preference and fail to limit the range of reflectance, the naturalness of non-uniform illumination images cannot be effectively preserved. However, naturalness is essential for image enhancement to achieve pleasing perceptual quality. In order to preserve naturalness while enhancing details, we propose an enhancement algorithm for non-uniform illumination images. In general, this paper makes the following three major contributions. First, a lightness-order-error measure is proposed to access naturalness preservation objectively. Second, a bright-pass filter is proposed to decompose an image into reflectance and illumination, which, respectively, determine the details and the naturalness of the image. Third, we propose a bi-log transformation, which is utilized to map the illumination to make a balance between details and naturalness. Experimental results demonstrate that the proposed algorithm can not only enhance the details but also preserve the naturalness for non-uniform illumination images.

Naturalness Preserved Enhancement Algorithm for Non-Uniform Illumination Images

Remote sensing with radar is typically an ill-posed linear inverse problem: a scene is to be inferred from limited measurements of scattered electric fields. Parsimonious models provide a compressed representation of the unknown scene and offer a means for regularizing the inversion task. The emerging field of compressed sensing combines nonlinear reconstruction algorithms and pseudorandom linear measurements to provide reconstruction guarantees for sparse solutions to linear inverse problems. This paper surveys the use of sparse reconstruction algorithms and randomized measurement strategies in radar processing. Although the two themes have a long history in radar literature, the accessible framework provided by compressed sensing illuminates the impact of joining these themes. Potential future directions are conjectured both for extension of theory motivated by practice and for modification of practice based on theoretical insights.

https://vpa.sabanciuniv.edu/vpadb/findfile_get_anonymous_paper.php?f=2011

Sparsity and Compressed Sensing in Radar Imaging

Since the light is absorbed and scattered while traveling in water, color distortion, under-exposure and fuzz are three major problems of underwater imaging. In this paper, a novel retinex-based enhancing approach is proposed to enhance single underwater image. The proposed approach has mainly three steps to solve the problems mentioned above. First, a simple but effective color correction strategy is adopted to address the color distortion. Second, a variational framework for retinex is proposed to decompose the reflectance and the illumination, which represent the detail and brightness respectively, from single underwater image. An effective alternating direction optimization strategy is adopted to solve the proposed model. Third, the reflectance and the illumination are enhanced by different strategies to address the under-exposure and fuzz problem. The final enhanced image is obtained by combining use the enhanced reflectance and illumination. The enhanced result is improved by color correction, lightens dark regions, naturalness preservation, and well enhanced edges and details. Moreover, the proposed approach is a general method that can enhance other kinds of degraded image, such as sandstorm image.

A retinex-based enhancing approach for single underwater image

[서평]「Chaos and Fractals : New Frontiers of Science」

The authors analysed a set of random frequency modulated (FM) signals for wideband radar imaging and assessed their resolution capability and sidelobe distribution on the range–Doppler plane. To this effect deterministic, bounded, nonlinear iterated maps were first considered. The initial condition of each chaotic map was assigned to a random variable to obtain statistically independent samples with invariant probability density function. The resulting sequences, which have white time–frequency representations, are used to construct wideband stochastic FM signals. These FM signals are ergodic and stationary. The autocorrelation, spectrum and the ambiguity surface associated with each of the FM signals were characterised. It was also demonstrated that the ambiguity surface of an FM signal generated via a chaotic map with uniform sample distribution and tail-shifted chaotic attractor is comparable to the ambiguity function of a Gaussian FM signal.

Assessment of chaos-based FM signals for range-Doppler imaging

From the Publisher:
Learn the newest processing techniques for focusing radar images with this important new book It helps you master the SAR/ISAR fundamentals that are critical to understanding motion compensation and advanced SAR/ISAR imaging techniques, and gives you the background you need to tackle problems such as estimating motion parameters by phase analysis, compensating the phase of a wideband signal, and processing a wideband signal into a radar image

In 14 chapters, with over 100 illustrations and nearly 300 equations, the authors introduce, develop and test methods for estimating the motion parameters of a target, and present an integrated approach for generating focused radar images of multiple moving targets illuminated by a radar beam Focusing on motion compensation of radar images, the book examines the development of filtering and reconstruction processes that allow for individual target motion compensation, discusses the implementation of this approach using the Gabor wavelet transform, and incorporates image enhancement techniques for the generation and identification of simulated and real aircraft images that cannot be obtained using conventional radar processors

Software Included: Diskette written in MATLAB allows you to simulate implementation of the techniques presented in the book, and to make modifications to the simulations to facilitate the understanding of these techniques System Requirements: IBM-compatible PC with 2 MB disk space

Range-Doppler Radar Imaging and Motion Compensation

Histogram specification has been successfully used in digital image processing over the years. Mainly used as an image enhancement technique, methods such as histogram equalization (HE) can yield good contrast with almost no effort in terms of inputs to the algorithm or the computational time required. More elaborate histograms can take on problems faced by HE at the expense of having to define the final histograms in innovative ways that may require some extra processing time but are nevertheless fast enough to be considered for real-time applications. This paper proposes a new technique for specifying a histogram to enhance the image contrast. To further evidence our faith on histogram specification techniques, we also discuss methods to modify images, e.g., to help segmentation approaches. Thus, as advocates of these techniques, we would like to emphasize the flexibility of this image processing approach to do more than enhancing images.

Histogram Specification: A Fast and Flexible Method to Process Digital Images

During lung sound recordings, heart sounds (HS) interfere with clinical interpretation of lung sounds over the low frequency components which is significant especially at low flow rates. Hence, it is desirable to cancel the effect of HS on lung sound records. In this paper, a novel HS cancellation method is presented. This method first localizes HS segments using multiresolution decomposition of the wavelet transform coefficients, then removes those segments from the original lung sound record and estimates the missing data via a 2D interpolation in the time-frequency (TF) domain. Finally, the signal is reconstructed into the time domain. To evaluate the efficiency of the TF filtering, the average power spectral density (PSD) of the original lung sound segments with and without HS over four frequency bands from 20 to 300 Hz were calculated and compared with the average PSD of the filtered signals. Statistical tests show that there is no significant difference between the average PSD of the HS-free original lung sounds and the TF-filtered signal for all frequency bands at both low and medium flow rates. It was found that the proposed method successfully removes HS from lung sound signals while preserving the original fundamental components of the lung sounds.

Heart sound cancellation from lung sound recordings using time-frequency filtering.

This paper presents a novel method for Heart Sound (HS) cancellation from Lung Sound (LS) records. The method uses the multiscale product of the wavelet coefficients of the original signal to detect HS-included segments. Once the HS segments are identified, the method removes them from the wavelet coefficients at every level and estimates the created gaps by using a set of linear prediction filters. It is shown that if the segment to be predicted is stationary, a final record with no audible artifacts such as clicks can be reconstructed using this approach. The results were promising for HS removal from LS records and showed no hampering of the main components of the LS. The results were confirmed both qualitatively by listening to the reconstructed signal and quantitatively by spectral analysis

Gabriel Thomas

Papers

Assessment of chaos-based FM signals for range-Doppler imaging

Range-Doppler Radar Imaging and Motion Compensation

Histogram Specification: A Fast and Flexible Method to Process Digital Images

Heart sound cancellation from lung sound recordings using time-frequency filtering.

Heart Sound Cancellation Based on Multiscale Products and Linear Prediction