Related papers: Simple, Efficient, and Neural Algorithms for Spars…
The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…
In exact sparse optimization problems on Rd (also known as sparsity constrained problems), one looks for solution that have few nonzero components. In this paper, we consider problems where sparsity is exactly measured either by the…
Non-negative sparse coding is a method for decomposing multivariate data into non-negative sparse components. In this paper we briefly describe the motivation behind this type of data representation and its relation to standard sparse…
Sparsifying neural networks often suffers from seemingly inevitable performance degradation, and it remains challenging to restore the original performance despite much recent progress. Motivated by recent studies in robust optimization, we…
Compressed sensing aims to undersample certain high-dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a…
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…
This paper treats the problem of minimizing a general continuously differentiable function subject to sparsity constraints. We present and analyze several different optimality criteria which are based on the notions of stationarity and…
Sparse approximation is important in many applications because of concise form of an approximant and good accuracy guarantees. The theory of compressed sensing, which proved to be very useful in the image processing and data sciences, is…
This short paper describes a simple coding technique, Sparse Sequential Dirichlet Coding, for multi-alphabet memoryless sources. It is appropriate in situations where only a small, unknown subset of the possible alphabet symbols can be…
The sparse linear regression problem is difficult to handle with usual sparse optimization models when both predictors and measurements are either quantized or represented in low-precision, due to non-convexity. In this paper, we provide a…
This paper investigates universal polar coding schemes. In particular, a notion of ordering (called convolutional path) is introduced between probability distributions to determine when a polar compression (or communication) scheme designed…
A large number of image super resolution algorithms based on the sparse coding are proposed, and some algorithms realize the multi-frame super resolution. In multi-frame super resolution based on the sparse coding, both accurate image…
We address the problem of decoding sparse quantum error correction codes. For Pauli channels, this task can be accomplished by a version of the belief propagation algorithm used for decoding sparse classical codes. Quantum codes pose two…
Exact recovery of a sparse solution for an underdetermined system of linear equations implies full search among all possible subsets of the dictionary, which is computationally intractable, while l1 minimization will do the job when a…
Representing signals with sparse vectors has a wide range of applications that range from image and video coding to shape representation and health monitoring. In many applications with real-time requirements, or that deal with…
Spreading the information over all coefficients of a representation is a desirable property in many applications such as digital communication or machine learning. This so-called antisparse representation can be obtained by solving a convex…
This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…
Sparse coding is a proven principle for learning compact representations of images. However, sparse coding by itself often leads to very redundant dictionaries. With images, this often takes the form of similar edge detectors which are…
It has recently been observed that certain extremely simple feature encoding techniques are able to achieve state of the art performance on several standard image classification benchmarks including deep belief networks, convolutional nets,…
In the blind deconvolution problem, we observe the convolution of an unknown filter and unknown signal and attempt to reconstruct the filter and signal. The problem seems impossible in general, since there are seemingly many more unknowns…