Related papers: A New Sparse SOS Decomposition Algorithm Based on …
This paper introduces a notion of decomposition and completion of sum-of-squares (SOS) matrices. We show that a subset of sparse SOS matrices with chordal sparsity patterns can be equivalently decomposed into a sum of multiple SOS matrices…
Two complementary approaches have been extensively used in signal and image processing leading to novel results, the sparse representation methodology and the variational strategy. Recently, a new sparsity based model has been proposed, the…
This paper proposes a subspace decomposition method based on an over-complete dictionary in sparse representation, called "Sparse Signal Subspace Decomposition" (or 3SD) method. This method makes use of a novel criterion based on the…
We provide a sparse version of the bounded degree SOS hierarchy BSOS [7] for polynomial optimization problems. It permits to treat large scale problems which satisfy a structured sparsity pattern. When the sparsity pattern satisfies the…
The sparse generalized eigenvalue problem arises in a number of standard and modern statistical learning models, including sparse principal component analysis, sparse Fisher discriminant analysis, and sparse canonical correlation analysis.…
Sparse optimization is a central problem in machine learning and computer vision. However, this problem is inherently NP-hard and thus difficult to solve in general. Combinatorial search methods find the global optimal solution but are…
In this paper, a fast algorithm for overcomplete sparse decomposition, called SL0, is proposed. The algorithm is essentially a method for obtaining sparse solutions of underdetermined systems of linear equations, and its applications…
This article addresses the image denoising problem in the situations of strong noise. We propose a dual sparse decomposition method. This method makes a sub-dictionary decomposition on the over-complete dictionary in the sparse…
A widely used method for solving SOS (Sum Of Squares) decomposition problem is to reduce it to the problem of semi-definite programs (SDPs) which can be efficiently solved in theory. In practice, although many SDP solvers can work out some…
This paper investigates a new learning formulation called structured sparsity, which is a natural extension of the standard sparsity concept in statistical learning and compressive sensing. By allowing arbitrary structures on the feature…
Cross-correlation is a popular signal processing technique used in numerous location tracking systems for obtaining reliable range information. However, its efficient design and practical implementation has not yet been achieved on mote…
This work proposes a new moment-SOS hierarchy, called CS-TSSOS, for solving large-scale sparse polynomial optimization problems. Its novelty is to exploit simultaneously correlative sparsity and term sparsity by combining advantages of two…
Sparse decomposition has been widely used for different applications, such as source separation, image classification and image denoising. This paper presents a new algorithm for segmentation of an image into background and foreground text…
In this paper an extension of the sparse decomposition problem is considered and an algorithm for solving it is presented. In this extension, it is known that one of the shifted versions of a signal s (not necessarily the original signal…
Optimization over non-negative polynomials is fundamental for nonlinear systems analysis and control. We investigate the relation between three tractable relaxations for optimizing over sparse non-negative polynomials: sparse sum-of-squares…
Sparsity-based methods are widely used in machine learning, statistics, and signal processing. There is now a rich class of structured sparsity approaches that expand the modeling power of the sparsity paradigm and incorporate constraints…
It is well-known that any sum of squares (SOS) program can be cast as a semidefinite program (SDP) of a particular structure and that therein lies the computational bottleneck for SOS programs, as the SDPs generated by this procedure are…
This work is a follow-up and a complement to arXiv:1912.08899 [math.OC] for solving polynomial optimization problems (POPs). The chordal-TSSOS hierarchy that we propose is a new sparse moment-SOS framework based on term-sparsity and chordal…
In compressed sensing, we wish to reconstruct a sparse signal $x$ from observed data $y$. In sparse coding, on the other hand, we wish to find a representation of an observed signal $y$ as a sparse linear combination, with coefficients $x$,…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…