Kevin Degraux | Searcharxiv

arXiv2017

Online Convolutional Dictionary Learning for Multimodal Imaging

Computational imaging methods that can exploit multiple modalities have the potential to enhance the capabilities of traditional sensing systems. In this paper, we propose a new method that reconstructs multimodal images from their linear measurements by exploiting redundancies across different modalities. Our method combines a convolutional group-sparse representation of images with total variation (TV) regularization for high-quality multimodal imaging. We develop an online algorithm that enables the unsupervised learning of convolutional dictionaries on large-scale datasets that are typical in such applications. We illustrate the benefit of our approach in the context of joint intensity-depth imaging.

cs.CV↗

arXiv2015

Consistent Basis Pursuit for Signal and Matrix Estimates in Quantized Compressed Sensing

This paper focuses on the estimation of low-complexity signals when they are observed through $M$ uniformly quantized compressive observations. Among such signals, we consider 1-D sparse vectors, low-rank matrices, or compressible signals that are well approximated by one of these two models. In this context, we prove the estimation efficiency of a variant of Basis Pursuit Denoise, called Consistent Basis Pursuit (CoBP), enforcing consistency between the observations and the re-observed estimate, while promoting its low-complexity nature. We show that the reconstruction error of CoBP decays like $M^{-1/4}$ when all parameters but $M$ are fixed. Our proof is connected to recent bounds on the proximity of vectors or matrices when (i) those belong to a set of small intrinsic "dimension", as measured by the Gaussian mean width, and (ii) they share the same quantized (dithered) random projections. By solving CoBP with a proximal algorithm, we provide some extensive numerical observations that confirm the theoretical bound as $M$ is increased, displaying even faster error decay than predicted. The same phenomenon is observed in the special, yet important case of 1-bit CS.

cs.IT↗