相关论文: An Open Problem on Sparse Representations in Union…
The fundamental principle underlying compressed sensing is that a signal, which is sparse under some basis representation, can be recovered from a small number of linear measurements. However, prior knowledge of the sparsity basis is…
Greedy algorithms for minimizing L0-norm of sparse decomposition have profound application impact on many signal processing problems. In the sparse coding setup, given the observations $\mathrm{y}$ and the redundant dictionary…
As shown by Tropp, 2008, for the concatenation of two orthonormal bases (ONBs), breaking the square-root bottleneck in compressed sensing does not require randomization over all the positions of the nonzero entries of the sparse coefficient…
Toric (or sparse) elimination theory is a framework developped during the last decades to exploit monomial structures in systems of Laurent polynomials. Roughly speaking, this amounts to computing in a \emph{semigroup algebra}, \emph{i.e.}…
The prototypical high-dimensional statistics problem entails finding a structured signal in noise. Many of these problems exhibit an intriguing phenomenon: the amount of data needed by all known computationally efficient algorithms far…
Many emerging applications involve sparse signals, and their processing is a subject of active research. We desire a large class of sensing matrices which allow the user to discern important properties of the measured sparse signal. Of…
In this paper, we consider a compressed sensing problem of reconstructing a sparse signal from an undersampled set of noisy linear measurements. The regularized least squares or least absolute shrinkage and selection operator (LASSO)…
Efficient sampling and approximation of Boltzmann distributions involving large sets of binary variables, or spins, are pivotal in diverse scientific fields even beyond physics. Recent advances in generative neural networks have…
Dictionary learning is the task of determining a data-dependent transform that yields a sparse representation of some observed data. The dictionary learning problem is non-convex, and usually solved via computationally complex iterative…
In compressed sensing sparse solutions are usually obtained by solving an $\ell^1$-minimization problem. Furthermore, the sparsity of the signal does need not be directly given. In fact, it is sufficient to have a signal that is sparse…
Sparse coding is a crucial subroutine in algorithms for various signal processing, deep learning, and other machine learning applications. The central goal is to learn an overcomplete dictionary that can sparsely represent a given input…
Finding a basis/coordinate system that can efficiently represent an input data stream by viewing them as realizations of a stochastic process is of tremendous importance in many fields including data compression and computational…
A linear equation $E$ is said to be sparse if there is $c>0$ so that every subset of $[n]$ of size $n^{1-c}$ contains a solution of $E$ in distinct integers. The problem of characterizing the sparse equations, first raised by Ruzsa in the…
This work develops a framework to discover relations between the components of the solution to a given initial-value problem for a first-order system of ordinary differential equations. This is done by using sparse identification techniques…
Inspired by the robustness and efficiency of sparse representation in sparse coding based image restoration models, we investigate the sparsity of neurons in deep networks. Our method structurally enforces sparsity constraints upon hidden…
This work investigates the problem of signal recovery from undersampled noisy sub-Gaussian measurements under the assumption of a synthesis-based sparsity model. Solving the $\ell^1$-synthesis basis pursuit allows for a simultaneous…
Demixing refers to the challenge of identifying two structured signals given only the sum of the two signals and prior information about their structures. Examples include the problem of separating a signal that is sparse with respect to…
A new paradigm in Sampling theory has been developed recently by Lu and Do. In this new approach the classical linear model is replaced by a non-linear, but structured model consisting of a union of subspaces. This is the natural approach…
Solving compressed sensing problems relies on the properties of sparse signals. It is commonly assumed that the sparsity s needs to be less than one half of the spark of the sensing matrix A, and then the unique sparsest solution exists,…
Finding sparse solutions of underdetermined systems of linear equations is a fundamental problem in signal processing and statistics which has become a subject of interest in recent years. In general, these systems have infinitely many…