convex optimization

Abstract: We consider the question of estimating a real low-complexity signal (such as a sparse vector or a low-rank matrix) from the phase of complex random measurements. We show that in this phase-only compressive sensing (PO-CS) scenario, we can perfectly recover such a signal with high probability and up to global unknown amplitude if the sensing matrix is a complex Gaussian random matrix and the number of measurements is large compared to the complexity level of the signal space.

Abstract: This paper investigates non-uniform guarantees of \(ell_1\) minimization, subject to an \(ell_infty\) data fidelity constraint, to stably recover the support of a sparse vector when solving noisy linear inverse problems.

Abstract: In this paper, we study the problem of recovering sparse or compressible signals from uniformly quantized measurements. We present a new class of convex optimization programs, or decoders, coined Basis Pursuit DeQuantizer of moment p (BPDQp), that model the quantization distortion more faithfully than the commonly used Basis Pursuit DeNoise (BPDN) program.

Abstract: This paper addresses the problem of localizing people in low and high density crowds with a network of heterogeneous cameras. The problem is recasted as a linear inverse problem. It relies on deducing the discretized occupancy vector of people on the ground, from the noisy binary silhouettes observed as foreground pixels in each camera.

Abstract: This short note studies a variation of the compressed sensing paradigm introduced recently by Vaswani et al., i.e., the recovery of sparse signals from a certain number of linear measurements when the signal support is partially known.

Abstract: We propose to evaluate our sparsity driven people localization framework on crowded complex scenes. The problem is recast as a linear inverse problem. It relies on deducing an occupancy vector, i.

Abstract: A generic approach is presented to detect and track people with a network of fixed and omnidirectional cameras given severely degraded foreground silhouettes. The problem is formulated as a sparsity constrained inverse problem.

Following the writing of my previous post, which obtained various interesting comments (many thanks to Gabriel Peyré, Igor Carron and Pierre Vandergheynst), I sent a mail to Michael P. Friedlander and Ewout van den Berg to point them this article and possibly obtain their point of views.

Recently, I was using the SPGL1 toolbox to recover some “compressed sensed” images. As a reminder, SPGL1 implements the method described in “Probing the Pareto Frontier for basis pursuit solutions” of Michael P.