Sparse signal restoration is usually formulated as the minimization of a quadratic cost function ‖y−Ax‖ 2 , where A is a dictionary and x is an unknown sparse vector. It is well-known that imposing an l0 constraint leads to an NP-hard minimization problem. The convex relaxation approach has received considerable attention, where the l0-norm is replaced by the l1-norm. Among the many efficient l...

A new framework is proposed for deriving adaptive algorithms for sparse channel estimation under the presence of Symmetric α-Stable (SαS) noise. The algorithmic framework employs the natural gradient and incorporates both the Lp norm of the channel prediction error and the L0 norm of the complex-valued channel taps. Based on this framework, a novel affine projection sign algorithm is derived an...

Nonnegative Matrix Factorization (NMF) is a standard tool for data analysis. An important variant is the Sparse NMF problem. A natural measure of sparsity is the L0 norm, however its optimization is NP-hard. Here, we consider a sparsity measure linear in the ratio of the L1 and L2 norms, and propose an efficient algorithm to handle the norm constraints which arise when optimizing this measure. ...

In this chapter, the authors propose a Super-Resolution (SR) method using a vector quantization codebook and filter dictionary. In the process of SR, we use the idea of compressive sensing to represent a sparsely sampled signal under the assumption that a combination of a small number of codewords can represent an image patch. A low-resolution image is obtained from an original high-resolution ...

Amplitude-versus-angle (AVA) inversion for pre-stack seismic data is a key technology in oil and gas reservoir prediction. Conventional AVA contains two main stages. Stage one estimates the relative change rates of P-wave velocity, S-wave velocity density, stage obtains density based on their through trace integration. An alternative way merges these stages to estimate directly. This less sensi...

In this paper we consider sparse approximation problems, that is, general l0 minimization problems with the l0-“norm” of a vector being a part of constraints or objective function. In particular, we first study the first-order optimality conditions for these problems. We then propose penalty decomposition (PD) methods for solving them in which a sequence of penalty subproblems are solved by a b...

In this paper, we propose a new method for synthetic aperture radar (SAR) image despeckling via L0-minimization strategy, which aims to smooth homogeneous areas while preserve significant structures in SAR images. We argue that the gradients of the despeckled images are sparse and can be pursued by L0-norm minimization. We then formularize the despeckling of SAR images as a global L0 optimizati...

In the Compressed Sensing (CS) framework, underdetermined system of linear equation (USLE) can have infinitely many possible solutions. However, we intend to find sparsest solution, which is l0-norm minimization. finding an l0 norm solution out solutions NP-hard problem that becomes non-convex optimization problem. It has been a practically proven fact penalty be adequately estimated by l1 norm...

Nonnegative matrix factorization (NMF) has become a ubiquitous tool for data analysis. An important variant is the sparse NMF problem which arises when we explicitly require the learnt features to be sparse. A natural measure of sparsity is the L0 norm, however its optimization is NP-hard. Mixed norms, such as L1/L2 measure, have been shown to model sparsity robustly, based on intuitive attribu...