# Compressed Sensing

### Multispectral Compressive Imaging Strategies Using Fabry–Pérot Filtered Sensors

Abstract: In this paper, we introduce two novel acquisition schemes for multispectral compressive imaging. Unlike most existing methods, the proposed computational imaging techniques do not include any dispersive element, as they use a dedicated sensor that integrates narrowband Fabry–Pérot spectral filters at the pixel level.

### Quantized Compressive K-Means

Abstract: The recent framework of compressive statistical learning proposes to design tractable learning algorithms that use only a heavily compressed representation - or sketch - of massive datasets. Compressive K-Means (CKM) is such a method: It aims at estimating the centroids of data clusters from pooled, nonlinear, and random signatures of the learning examples.

### A greedy blind calibration method for compressed sensing with unknown sensor gains

Abstract: The realisation of sensing modalities based on the principles of compressed sensing is often hindered by discrepancies between the mathematical model of its sensing operator, which is necessary during signal recovery, and its actual physical implementation, which can amply differ from the assumed model.

### On the Noise Robustness of Simultaneous Orthogonal Matching Pursuit

Abstract: In this paper, the joint support recovery of several sparse signals whose supports present similarities is examined. Each sparse signal is acquired using the same noisy linear measurement process, which returns fewer observations than the dimension of the sparse signals.

### Small Width, Low Distortions: Quantized Random Embeddings of Low-complexity Sets

Abstract: Under which conditions and with which distortions can we preserve the pairwise-distances of low-complexity vectors, e.g., for structured sets such as the set of sparse vectors or the one of low-rank matrices, when these are mapped in a finite set of vectors?

### Non-Convex Blind Calibration for Compressed Sensing via Iterative Hard Thresholding

Abstract: Real-world applications of compressed sensing are often limited by modelling errors between the sensing operator, which is necessary during signal recovery, and its actual physical implementation. In this paper we tackle the biconvex problem of recovering a sparse input signal jointly with some unknown and unstructured multiplicative factors affecting the sensors that capture each measurement.

### On The Exact Recovery Condition of Simultaneous Orthogonal Matching Pursuit

Abstract: Several exact recovery criteria (ERC) ensuring that orthogonal matching pursuit (OMP) identifies the correct support of sparse signals have been developed in the last few years. These ERC rely on the restricted isometry property (RIP), the associated restricted isometry constant (RIC) and sometimes the restricted orthogonality constant (ROC).

### Quasi-isometric embeddings of vector sets with quantized sub-Gaussian projections

Last January, I was honored to be invited in RWTH Aachen University by Holger Rauhut and Sjoerd Dirksen to give a talk on the general topic of quantized compressed sensing. In particular, I decided to focus my presentation on the quasi-isometric embeddings arising in 1-bit compressed sensing, as developed by a few researchers in this field (e.

### Quasi-isometric embeddings of vector sets with quantized sub-Gaussian projections


### A Quantized Johnson Lindenstrauss Lemma: The Finding of Buffon's Needle

Abstract: In 1733, Georges-Louis Leclerc, Comte de Buffon in France, set the ground of geometric probability theory by defining an enlightening problem: What is the probability that a needle thrown randomly on a ground made of equispaced parallel strips lies on two of them?