Compressive Sensing

Signal Processing after quadratic sketching
Sketching is a commonly used technique in signal processing. In this short piece we describe how to estimate functions of a given signal based solely on its sketch and without explicit reconstruction.
Nov 20, 2023

Compressive Fourier Transform Interferometry for Hyperspectral Imaging
In this project we propose two variants of the Fourier Transform Interferometry (FTI) imager, i.e., coded illumination-FTI (CI-FTI) and structured illumination FTI (SI-FTI), based on the theory of compressive sensing (CS). These schemes efficiently modulate light exposure temporally (in CI-FTI) or spatiotemporally (in SI-FTI). Leveraging a variable density sampling strategy recently introduced in CS, we provide near-optimal illumination strategies, so that the light exposure imposed on a biological specimen is minimized while the spectral resolution is preserved.
Mar 3, 2020
Compressive Hadamard Sensing with Haar Sparsity Basis
In this project, we compute an explicit sample-complexity bound for Hadamard-Haar systems as well as uniform and nonuniform recovery guarantees.
Mar 2, 2020
Compressive Lensless Speckle Imaging
The lensless endoscope (LE) is a promising device to acquire _in vivo_ biological images at a cellular scale. In addition to its high resolution, the tiny size of the probe allows a deep exploration of the tissues. This research aims at exploring acquisition strategies inspired by the compressive sampling theory and relying on two key properties of the LE: (_i_) the ability to easily generate unstructured illumination patterns by randomly programming the spatial light modulator and (_ii_) the robustness of the fiber to spatial and temporal distortion allowing the use of fast galvanometer mirrors to shift light patterns.
Feb 28, 2020
Compressive Learning
This is a collection of sub-projects gravitating around the field of Compressive (Statistical) Learning, a machine learning framework that uses inspiration from compressive sensing to relieve to computational load of learning from massive datasets.
Jan 15, 2020

Consistent Basis Pursuit in Quantized Compressed Sensing
This project 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.
Oct 1, 2015

Compressive Schlieren Deflectometry
This project concerns with the application of compressive sensing principles for characterizing transparent objects using schlieren deflectometry. This is an instance of real world applications of compressed sensing.
Sep 17, 2014