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.

Through the Haze: a Non-Convex Approach to Blind Gain Calibration for Linear Random Sensing Models

Abstract: Computational sensing strategies often suffer from calibration errors in the physical implementation of their ideal sensing models. Such uncertainties are typically addressed by using multiple, accurately chosen training signals to recover the missing information on the sensing model, an approach that can be resource-consuming and cumbersome.

Discriminative and efficient label propagation on complementary graphs for multi-object tracking

Abstract: Given a set of detections, detected at each time instant independently, we investigate how to associate them across time. This is done by propagating labels on a set of graphs, each graph capturing how either the spatiotemporal or the appearance cues promote the assignment of identical or distinct labels to a pair of detections.

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?

Time for dithering: fast and quantized random embeddings via the restricted isometry property

Abstract: Recently, many works have focused on the characterization of non-linear dimensionality reduction methods obtained by quantizing linear embeddings, e.g., to reach fast processing time, efficient data compression procedures, novel geometry-preserving embeddings or to estimate the information/bits stored in this reduced data representation.

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.

Improving the Correlation Lower Bound for Simultaneous Orthogonal Matching Pursuit

Abstract: The simultaneous orthogonal matching pursuit (SOMP) algorithm aims to find the joint support of a set of sparse signals acquired under a multiple measurement vector model. Critically, the analysis of SOMP depends on the maximal inner product of any atom of a suitable dictionary and the current signal residual, which is formed by the subtraction of previously selected atoms.

Non-parametric PSF estimation from celestial transit solar images using blind deconvolution

Context: Characterization of instrumental effects in astronomical imaging is important in order to extract accurate physical information from the observations. The measured image in a real optical instrument is usually represented by the convolution of an ideal image with a Point Spread Function (PSF).