An Inexact Penalty Decomposition Method for Sparse Optimization

The penalty decomposition method is an effective and versatile method for sparse optimization and has been successfully applied to solve compressed sensing, sparse logistic regression, sparse inverse covariance selection, low rank minimization, image restoration, and so on. With increase in the penalty parameters, a sequence of penalty subproblems required being solved by the penalty decomposition method may be time consuming. In this paper, an acceleration of the penalty decomposition method is proposed for the sparse optimization problem. For each penalty parameter, this method just finds some inexact solutions to those subproblems. Computational experiments on a number of test instances demonstrate the effectiveness and efficiency of the proposed method in accurately generating sparse and redundant representations of one-dimensional random signals.

Interferometric SAR Phase Denoising Using Proximity-Based K-SVD Technique

This paper addresses the problem of interferometric noise reduction in Synthetic Aperture Radar (SAR) interferometry based on sparse and redundant representations over a trained dictionary. The idea is to use a Proximity-based K-SVD (ProK-SVD) algorithm on interferometric data for obtaining a suitable dictionary, in order to extract the phase image content effectively. We implemented this strategy on both simulated as well as real interferometric data for the validation of our approach. For synthetic data, three different training dictionaries have been compared, namely, a dictionary extracted from the data, a dictionary obtained by a uniform random distribution in [ − π , π ] , and a dictionary built from discrete cosine transform. Further, a similar strategy plan has been applied to real interferograms. We used interferometric data of various SAR sensors, including low resolution C-band ERS/ENVISAT, medium L-band ALOS, and high resolution X-band COSMO-SkyMed, all over an area of Mt. Etna, Italy. Both on simulated and real interferometric phase images, the proposed approach shows significant noise reduction within the fringe pattern, without any considerable loss of useful information.

On the Redundant Representation of Partial Remainders in Radix-4 SRT Dividers

Most digit-recurrence algorithms for division, such as the Sweeney–Robertson–Tocher (SRT) algorithm, have been used in order to take advantage of the redundant representations of the partial remainder. This way, full carry propagate additions are avoided, obtaining significant latency improvements. Furthermore, the delay corresponding to one division iteration is independent of the size of the operands. The most frequent redundant form for the partial remainders is the carry-save (CS) representation, which uses 2 bits of representation (carry and sum bits) for each bit of the partial remainder. This paper proposes radix-4 SRT dividers which use (3, 2) redundancy (3 bits of representation for 2 bits of the partial remainder) and (5, 4) redundancy (5 bits of representation for 4 bits of the partial remainder). The goal of using these representations is represented by a decreased cost due to the reduced number of sequential elements required to store the partial remainder. The proposed dividers use 2-bit carry propagate adders and 4-bit carry propagate adders to compute the new partial remainder. Thus, the full carry propagate addition is avoided, while the latency of one division iteration is independent of the operands’ size. The synthesis result for Xilinx Virtex-5 FPGA devices show that similar working frequencies are obtained for divider using the proposed redundant representation with respect to the conventional carry-save, while requiring up to 12% for (3, 2) representation and 18% for (5, 4) representation less sequential elements.

Image and Video Restoration and Enhancement via Sparse Representation

The chapter provides a survey of recent advances in image/video restoration and enhancement via spare representation. Images/videos usually unavoidably suffer from noises due to sensor imperfection or poor illumination. Numerous contributions have addressed this problem from diverse points of view. Recently, the use of sparse and redundant representations over learned dictionaries has become one specific approach. One goal here is to provide a survey of advances in image/video denoising via sparse representation. Moreover, to consider more general types of noise, this chapter also addresses the problems about removals of structured/unstructured components (e.g., rain streaks or blocking artifacts) from image/video. Moreover, image/video quality may be degraded from low-resolution due to low-cost acquisition. Hence, this chapter also provides a survey of recently advances in super-resolution via sparse representation. Finally, the conclusion can be drawn that sparse representation techniques have been reliable solutions in several problems of image/video restoration and enhancement.

GF(2n) Redundant Representation Using Matrix Embedding for Irreducible Trinomials

By embedding a Toeplitz matrix-vector product (MVP) of dimension n into a circulant MVP of dimension [Formula: see text], where δ can be any nonnegative integer, we present a GF(2n) multiplication algorithm. This algorithm leads to a new redundant representation, and it has two merits: (1) The flexible choices of δ make it possible to select a proper N such that the multiplication operation in ring [Formula: see text] can be performed using some asymptotically faster algorithms, e.g. the Fast Fourier Transformation (FFT)-based multiplication algorithm; (2) The redundant degrees, which are defined as N/n, are smaller than those of most previous GF(2n) redundant representations, and in fact they are approximately equal to 2 for all applicable cases.

Image and Video Restoration and Enhancement via Sparse Representation

The chapter provides a survey of recent advances in image/video restoration and enhancement via spare representation. Images/videos usually unavoidably suffer from noises due to sensor imperfection or poor illumination. Numerous contributions have addressed this problem from diverse points of view. Recently, the use of sparse and redundant representations over learned dictionaries has become one specific approach. One goal here is to provide a survey of advances in image/video denoising via sparse representation. Moreover, to consider more general types of noise, this chapter also addresses the problems about removals of structured/unstructured components (e.g., rain streaks or blocking artifacts) from image/video. Moreover, image/video quality may be degraded from low-resolution due to low-cost acquisition. Hence, this chapter also provides a survey of recently advances in super-resolution via sparse representation. Finally, the conclusion can be drawn that sparse representation techniques have been reliable solutions in several problems of image/video restoration and enhancement.