Related papers: Thouless-Anderson-Palmer Approach for Lossy Compre…
We propose computationally efficient encoders and decoders for lossy compression using a Sparse Regression Code. The codebook is defined by a design matrix and codewords are structured linear combinations of columns of this matrix. The…
This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the…
We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn from an invariant random matrix…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…
Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due…
Inverse imaging problems that are ill-posed can be encountered across multiple domains of science and technology, ranging from medical diagnosis to astronomical studies. To reconstruct images from incomplete and distorted data, it is…
A lossy compression algorithm for binary redundant memoryless sources is presented. The proposed scheme is based on sparse graph codes. By introducing a nonlinear function, redundant memoryless sequences can be compressed. We propose a…
Motivated by applications in unsourced random access, this paper develops a novel scheme for the problem of compressed sensing of binary signals. In this problem, the goal is to design a sensing matrix $A$ and a recovery algorithm, such…
Motivated by the question of optimal functional approximation via compressed sensing, we propose generalizations of the Iterative Hard Thresholding and the Compressive Sampling Matching Pursuit algorithms able to promote sparse in levels…
In the context of the compressed sensing problem, we propose a new ensemble of sparse random matrices which allow one (i) to acquire and compress a {\rho}0-sparse signal of length N in a time linear in N and (ii) to perfectly recover the…
Sparse representation using over-complete dictionaries have shown to produce good quality results in various image processing tasks. Dictionary learning algorithms have made it possible to engineer data adaptive dictionaries which have…
We begin by presenting a simple lossy compressor operating at near-zero rate: The encoder merely describes the indices of the few maximal source components, while the decoder's reconstruction is a natural estimate of the source components…
We characterize the effectiveness of a classical algorithm for recovering the Markov graph of a general discrete pairwise graphical model from i.i.d. samples. The algorithm is (appropriately regularized) maximum conditional log-likelihood,…
We propose an iterative algorithm for solving the Thouless-Anderson-Palmer (TAP) equations of Ising models with arbitrary rotation invariant (random) coupling matrices. In the thermodynamic limit, we prove by means of the dynamical…
The choice of the sensing matrix is crucial in compressed sensing. Random Gaussian sensing matrices satisfy the restricted isometry property, which is crucial for solving the sparse recovery problem using convex optimization techniques.…
We consider a prototypical problem of Bayesian inference for a structured spiked model: a low-rank signal is corrupted by additive noise. While both information-theoretic and algorithmic limits are well understood when the noise is a…
Tucker decomposition is the cornerstone of modern machine learning on tensorial data analysis, which have attracted considerable attention for multiway feature extraction, compressive sensing, and tensor completion. The most challenging…
We present the framework of slowly varying regression under sparsity, allowing sparse regression models to exhibit slow and sparse variations. The problem of parameter estimation is formulated as a mixed-integer optimization problem. We…
Autoencoders are a prominent model in many empirical branches of machine learning and lossy data compression. However, basic theoretical questions remain unanswered even in a shallow two-layer setting. In particular, to what degree does a…
We propose a sparse algebra for samplet compressed kernel matrices, to enable efficient scattered data analysis. We show the compression of kernel matrices by means of samplets produces optimally sparse matrices in a certain S-format. It…