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A panorama on multiscale geometric representations, intertwining spatial, directional and frequency selectivity

More information: This paper is part of the special issue “Advances in Multirate Filter Bank Structures and Multiscale Representations.” Here is a webpage related to this work (on Laurent Duval’s website).

Dequantizing Compressed Sensing: When Oversampling and Non-Gaussian Constraints Combine

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.

Sparsity Driven People Localization with a Heterogeneous Network of Cameras

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.

A short note on compressed sensing with partially known signal support

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.

Compressed sensing imaging techniques for radio interferometry

Abstract: Radio interferometry probes astrophysical signals through incomplete and noisy Fourier measurements. The theory of compressed sensing demonstrates that such measurements may actually suffice for accurate reconstruction of sparse or compressible signals.

A geometrical study of matching pursuit parametrization

Abstract: This paper studies the effect of discretizing the parametrization of a dictionary used for matching pursuit (MP) decompositions of signals. Our approach relies con viewing the continuously parametrized dictionary as an embedded manifold in the signal space on which the tools of differential, (Riemannian) geometry can be applied.

Fast spin $\pm 2$ spherical harmonics transforms and application in cosmology

Abstract: A fast and exact algorithm is developed for the spin \(\pm2\) spherical harmonics transforms on equi-angular pixelizations on the sphere. It is based on the Driscoll and Healy fast scalar spherical harmonics transform.

Multiselective pyramidal decomposition of images: Wavelets with adaptive angular selectivity

Abstract: Many techniques have been devised these last ten years to add an appropriate directionality concept in decompositions of images from the specific transformations of a small set of atomic functions.