Related papers: Rateless Lossy Compression via the Extremes
Marton's optimal error exponent for the lossy source coding problem is defined as a non-convex optimization problem. This fact had prevented us to develop an efficient algorithm to compute it. This problem is caused by the fact that the…
Belief propagation applied to iterative decoding and sparse recovery through approximate message passing (AMP) are two research areas that have seen monumental progress in recent decades. Inspired by these advances, this article introduces…
We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
Decentralized sparsity learning has attracted a significant amount of attention recently due to its rapidly growing applications. To obtain the robust and sparse estimators, a natural idea is to adopt the non-smooth median loss combined…
We present a simple and effective algorithm for the problem of \emph{sparse robust linear regression}. In this problem, one would like to estimate a sparse vector $w^* \in \mathbb{R}^n$ from linear measurements corrupted by sparse noise…
We revisit the source image estimation problem from blind source separation (BSS). We generalize the traditional minimum distortion principle to maximum likelihood estimation with a model for the residual spectrograms. Because residual…
We propose a universal ensemble for random selection of rate-distortion codes, which is asymptotically optimal in a sample-wise sense. According to this ensemble, each reproduction vector, $\hbx$, is selected independently at random under…
Sparse coding aims to model data vectors as sparse linear combinations of basis elements, but a majority of related studies are restricted to continuous data without spatial or temporal structure. A new model-based sparse coding (MSC)…
As a fundamental data format representing spatial information, depth map is widely used in signal processing and computer vision fields. Massive amount of high precision depth maps are produced with the rapid development of equipment like…
Consider a pair of correlated Gaussian sources (X1,X2). Two separate encoders observe the two components and communicate compressed versions of their observations to a common decoder. The decoder is interested in reconstructing a linear…
This paper provides an extensive study of the behavior of the best achievable rate (and other related fundamental limits) in variable-length lossless compression. In the non-asymptotic regime, the fundamental limits of fixed-to-variable…
We propose two novel approaches to the recovery of an (approximately) sparse signal from noisy linear measurements in the case that the signal is a priori known to be non-negative and obey given linear equality constraints, such as simplex…
To fill the gap of traditional GS compression method, in this paper, we first propose a simple and effective GS data compression anchor called Graph-based GS Compression (GGSC). GGSC is inspired by graph signal processing theory and uses…
This note studies a method for the efficient estimation of a finite number of unknown parameters from linear equations, which are perturbed by Gaussian noise. In case the unknown parameters have only few nonzero entries, the proposed…
Compressed sensing allows for the recovery of sparse signals from few measurements, whose number is proportional to the sparsity of the unknown signal, up to logarithmic factors. The classical theory typically considers either random linear…
We study high-dimensional least-squares regression within a subgaussian statistical learning framework with heterogeneous noise. It includes $s$-sparse and $r$-low-rank least-squares regression when a fraction $\epsilon$ of the labels are…
Sparse coding is an unsupervised learning algorithm that learns a succinct high-level representation of the inputs given only unlabeled data; it represents each input as a sparse linear combination of a set of basis functions. Originally…
Sparse superposition codes were originally proposed as a capacity-achieving communication scheme over the gaussian channel, whose coding matrices were made of i.i.d. gaussian entries.We extend this coding scheme to more generic ensembles of…
This paper studies the rate-distortion-perception (RDP) tradeoff for a memoryless source model in the asymptotic limit of large block-lengths. The perception measure is based on a divergence between the distributions of the source and…