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The Importance of Phase in Complex Compressive Sensing

Abstract: We consider the question of estimating a real low-complexity signal (such as a sparse vector or a low-rank matrix) from the phase of complex random measurements. We show that in this phase-only compressive sensing (PO-CS) scenario, we can perfectly recover such a signal with high probability and up to global unknown amplitude if the sensing matrix is a complex Gaussian random matrix and the number of measurements is large compared to the complexity level of the signal space.

$(\ell_{1},\ell_{2})$-RIP and Projected Back-Projection Reconstruction for Phase-Only Measurements

Abstract: This letter analyzes the performances of a simple reconstruction method, namely the Projected Back-Projection (PBP), for estimating the direction of a sparse signal from its phase-only (or amplitude-less) complex Gaussian random measurements, i.

Close Encounters of the Binary Kind: Signal Reconstruction Guarantees for Compressive Hadamard Sampling with Haar Wavelet Basis

Abstract: We investigate the problems of 1-D and 2-D signal recovery from subsampled Hadamard measurements using Haar wavelet as a sparsity inducing prior. These problems are of interest in, e.g., computational imaging applications relying on optical multiplexing or single-pixel imaging.

Hardware-Compliant Compressive Image Sensor Architecture Based on Random Modulations and Permutations for Embedded Inference

Abstract: This work presents a compact CMOS Image Sensor (CIS) architecture enabling embedded object recognition facilitated by a dedicated end-of-column Compressive Sensing (CS), reducing on-chip memory needs. Our sensing scheme is based on a combination of random modulations and permutations leading to an implementation with very limited hardware impacts.

A Variable Density Sampling Scheme for Compressive Fourier Transform Interferometry

Abstract: Fourier Transform Interferometry (FTI) is an appealing Hyperspectral (HS) imaging modality for many applications demanding high spectral resolution, e.g., in fluorescence microscopy. However, the effective resolution of FTI is limited by the durability of biological elements when exposed to illuminating light.

Jointly low-rank and bisparse recovery: Questions and partial answers

Abstract: We investigate the problem of recovering jointly \(r\)-rank and \(s\)-bisparse matrices from as few linear measurements as possible, considering arbitrary measurements as well as rank-one measurements. In both cases, we show that \(m \asymp r s \ln(en/s)\) measurements make the recovery possible in theory, meaning via a nonpractical algorithm.

Quantized Compressive Sensing with RIP Matrices: The Benefit of Dithering

Abstract: Quantized compressive sensing (QCS) deals with the problem of coding compressive measurements of low-complexity signals with quantized, finite precision representations, i.e., a mandatory process involved in any practical sensing model.

STIM map: detection map for exoplanets imaging beyond asymptotic Gaussian residual speckle noise

Abstract: Direct imaging of exoplanets is a challenging task as it requires to reach a high contrast at very close separation to the star. Today, the main limitation in the high-contrast images is the quasi-static speckles that are created by residual instrumental aberrations.

Determination of vibration amplitudes from binary phase patterns obtained by phase-shifting time-averaged speckle shearing interferometry

Abstract: Speckle shearing interferometry (shearography) is a full-field strain measurement technique that can be used in vibration analysis. In our case, we apply a method that combines the time-averaging and phase-shifting techniques.

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.