Related papers: Optimized Compressed Sensing via Incoherent Frames…
In compressed sensing a sparse vector is approximately retrieved from an under-determined equation system $Ax=b$. Exact retrieval would mean solving a large combinatorial problem which is well known to be NP-hard. For $b$ of the form…
So far there has not been paid attention to frames that are balanced, i.e. those frames which sum is zero. In this paper we consider balanced frames, and in particular balanced unit norm tight frames, in finite dimensional Hilbert spaces.…
Proximal gradient methods are popular in sparse optimization as they are straightforward to implement. Nevertheless, they achieve biased solutions, requiring many iterations to converge. This work addresses these issues through a suitable…
In this paper, we generalize the chance optimization problems and introduce constrained volume optimization where enables us to obtain convex formulation for challenging problems in systems and control. We show that many different problems…
We present an end-to-end image compression system based on compressive sensing. The presented system integrates the conventional scheme of compressive sampling and reconstruction with quantization and entropy coding. The compression…
We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize…
The breakthrough ideas in the modern proximal splitting methodologies allow us to express the set of all minimizers of a superposition of multiple nonsmooth convex functions as the fixed point set of computable nonexpansive operators. In…
This paper is devoted to general nonconvex problems of multiobjective optimization in Hilbert spaces. Based on Mordukhovich's limiting subgradients, we define a new notion of Pareto critical points for such problems, establish necessary…
Recent work has shown that learned image compression strategies can outperform standard hand-crafted compression algorithms that have been developed over decades of intensive research on the rate-distortion trade-off. With growing…
The compressive sensing (CS) and 1-bit CS demonstrate superior efficiency in signal acquisition and resource conservation, while 1-bit CS achieves maximum resource efficiency through sign-only measurements. With the emergence of massive…
Compressive Learning is an emerging topic that combines signal acquisition via compressive sensing and machine learning to perform inference tasks directly on a small number of measurements. Many data modalities naturally have a…
This work proposes and analyzes a compressed sensing approach to polynomial approximation of complex-valued functions in high dimensions. Of particular interest is the setting where the target function is smooth, characterized by a rapidly…
Convexity prior is one of the main cue for human vision and shape completion with important applications in image processing, computer vision. This paper focuses on characterization methods for convex objects and applications in image…
We study distributed composite optimization over networks: agents minimize a sum of smooth (strongly) convex functions, the agents' sum-utility, plus a nonsmooth (extended-valued) convex one. We propose a general unified algorithmic…
In this paper, we present the Monte-Carlo Compressive Optimization algorithm, a new method to solve a combinatorial optimization problem that is assumed compressible. The method relies on random queries to the objective function in order to…
We provide the first analysis of a non-trivial quantization scheme for compressed sensing measurements arising from structured measurements. Specifically, our analysis studies compressed sensing matrices consisting of rows selected at…
Optical coherence tomography (OCT) is an important interferometric diagnostic technique which provides cross-sectional views of the subsurface microstructure of biological tissues. However, the imaging quality of high-speed OCT is limited…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
In this era of big data, data analytics and machine learning, it is imperative to find ways to compress large data sets such that intrinsic features necessary for subsequent analysis are not lost. The traditional workhorse for data…