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A novel framework of compressed sensing, namely statistical compressed sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution, and achieving accurate reconstruction on average, is…
We present optimal sample complexity estimates for one-bit compressed sensing problems in a realistic scenario: the procedure uses a structured matrix (a randomly sub-sampled circulant matrix) and is robust to analog pre-quantization noise…
Explicitly using the block structure of the unknown signal can achieve better reconstruction performance in compressive sensing. Theoretically, an unknown signal with block structure can be accurately recovered from a few number of…
Frequency estimation from measurements corrupted by noise is a fundamental challenge across numerous engineering and scientific fields. Among the pivotal factors shaping the resolution capacity of any frequency estimation technique are…
Quantum phase estimation is a paradigmatic problem in quantum sensing andmetrology. Here we show that adaptive methods based on classical machinelearning algorithms can be used to enhance the precision of quantum phase estimation when noisy…
We address the metrological problem of estimating collective stochastic properties imprinted on a network of quantum sensors. Canonical examples include center-of-mass quadrature fluctuations in a system of bosonic modes and correlated…
The problem of recovering the sparsity pattern of a fixed but unknown vector $\beta^* \in \real^p based on a set of $n$ noisy observations arises in a variety of settings, including subset selection in regression, graphical model selection,…
We consider the problem of sparse signal reconstruction from noisy one-bit compressed measurements when the receiver has access to side-information (SI). We assume that compressed measurements are corrupted by additive white Gaussian noise…
We discuss two new methods of recovery of sparse signals from noisy observation based on $\ell_1$- minimization. They are closely related to the well-known techniques such as Lasso and Dantzig Selector. However, these estimators come with…
Compressed sensing is a theory which guarantees the exact recovery of sparse signals from a small number of linear projections. The sampling schemes suggested by current compressed sensing theories are often of little practical relevance…
Existing convex relaxation-based approaches to reconstruction in compressed sensing assume that noise in the measurements is independent of the signal of interest. We consider the case of noise being linearly correlated with the signal and…
Compressed Sensing (CS) is an appealing framework for applications such as Magnetic Resonance Imaging (MRI). However, up-to-date, the sensing schemes suggested by CS theories are made of random isolated measurements, which are usually…
We study the use of very sparse random projections for compressed sensing (sparse signal recovery) when the signal entries can be either positive or negative. In our setting, the entries of a Gaussian design matrix are randomly sparsified…
Compressed sensing enables sparse sampling but relies on generic bases and random measurements, limiting efficiency and reconstruction quality. Optimal sensor placement uses historcal data to design tailored sampling patterns, yet its…
We consider a resource-limited scenario where a sensor that uses compressed sensing (CS) collects a low number of measurements in order to observe a sparse signal, and the measurements are subsequently quantized at a low bit-rate followed…
The one-bit quantization is implemented by one single comparator that operates at low power and a high rate. Hence one-bit compressive sensing (1bit-CS) becomes attractive in signal processing. When measurements are corrupted by noise…
This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A…
We introduce a recursive algorithm for performing compressed sensing on streaming data. The approach consists of a) recursive encoding, where we sample the input stream via overlapping windowing and make use of the previous measurement in…
Minimum mean square error (MMSE) estimation of block sparse signals from noisy linear measurements is considered. Unlike in the standard compressive sensing setup where the non-zero entries of the signal are independently and uniformly…
Compressed sensing (CS) is about recovering a structured signal from its under-determined linear measurements. Starting from sparsity, recovery methods have steadily moved towards more complex structures. Emerging machine learning tools…