A Non-Convex Approach to Blind Calibration for Linear Random Sensing Models

Abstract: Performing blind calibration is highly important in modern sensing strategies, particularly when calibration aided by multiple, accurately designed training signals is infeasible or resource-consuming. We here address it as a naturally-formulated non-convex problem for a linear model with sub-Gaussian ran- dom sensing vectors in which both the sensor gains and the sig- nal are unknown.

A Non-Convex Approach to Blind Calibration from Linear Sub-Gaussian Random Measurements

Abstract: Blind calibration is a bilinear inverse problem arising in modern sensing strategies, whose solution becomes crucial when traditional calibration aided by multiple, accurately designed training signals is either infeasible or resource-consuming.

A non-convex blind calibration method for randomised sensing strategies

Abstract: The implementation of computational sensing strategies often faces calibration problems typically solved by means of multiple, accurately chosen training signals, an approach that can be resource-consuming and cumbersome. Conversely, blind calibration does not require any training, but corresponds to a bilinear inverse problem whose algorithmic solution is an open issue.

Compressive Hyperspectral Imaging with Fourier Transform Interferometry

Abstract: This paper studies the fast acquisition of Hyper- Spectral (HS) data using Fourier transform interferometry (FTI). FTI has emerged as a promising alternative to capture, at a very high resolution, the wavelength coordinate as well as the spatial domain of the HS volume.

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

Abstract: 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.

Error Decay of (almost) Consistent Signal Estimations from Quantized Gaussian Random Projections

Abstract: This paper provides new error bounds on “consistent” reconstruction methods for signals observed from quantized random projections. Those signal estimation techniques guarantee a perfect matching between the available quantized data and a new observation of the estimated signal under the same sensing model.

Low Rank and Group-Average Sparsity Driven Convex Optimization for Direct Exoplanets Imaging

Abstract: Direct exoplanets imaging is a challenging task for two main reasons. First, the host star is several order of magnitude brighter than exoplanets. Second, the great distance between us and the star system makes the exoplanets-star angular dis- tance very small.

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.

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?