Inverse Problem
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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
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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 work, 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 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.Oct 23, 2017 -
Compressive Optical Deflectometric Tomography
The refractive index map allows the optical characterization of complex transparent materials such as optical fibers or intraocular lenses. This research topic addresses the problem of reconstructing the refractive index map of a transparent object from few amount of optical deflectometric measurements. We aim at developing a numerical reconstruction method which makes Optical Deflectometric Tomography compressive and robust to noise.Sep 19, 2017 -
Bilinear and Biconvex Inverse Problems for Computational Sensing Systems
A research effort in the solution of blind calibration and deconvolution problems arising in compressive imaging.Sep 19, 2017
