Related papers: Local recovery bounds for prior support constraine…
In this paper, we study the support recovery conditions of weighted $\ell_1$ minimization for signal reconstruction from compressed sensing measurements when multiple support estimate sets with different accuracy are available. We identify…
The theory of Compressed Sensing, the emerging sampling paradigm 'that goes against the common wisdom', asserts that 'one can recover signals in Rn from far fewer samples or measurements, if the signal has a sparse representation in some…
Sparsity is a ubiquitous feature of many real world signals such as natural images and neural spiking activities. Conventional compressed sensing utilizes sparsity to recover low dimensional signal structures in high ambient dimensions…
The restricted isometry property (RIP) has become well-known in the compressed sensing community. Recently, a weaken version of RIP was proposed for exact sparse recovery under weak moment assumptions. In this note, we prove that the weaken…
We study the recovery conditions of weighted $\ell_1$ minimization for real-valued signal reconstruction from phaseless compressive sensing measurements when partial support information is available. A strong restricted isometry property…
Optimal designs for generalized linear models require a prior knowledge of the regression parameters. At certain values of the parameters we propose particular assumptions which allow to derive a locally optimal design for a model without…
Within the Compressive Sensing (CS) paradigm, sparse signals can be reconstructed based on a reduced set of measurements. Reliability of the solution is determined by the uniqueness condition. With its mathematically tractable and feasible…
Large-scale data collection by means of wireless sensor network and internet-of-things technology poses various challenges in view of the limitations in transmission, computation, and energy resources of the associated wireless devices.…
A compressed sensing method consists of a rectangular measurement matrix, $M \in \mathbbm{R}^{m \times N}$ with $m \ll N$, together with an associated recovery algorithm, $\mathcal{A}: \mathbbm{R}^m \rightarrow \mathbbm{R}^N$. Compressed…
Compressed Sensing (CS) is an emerging field that enables reconstruction of a sparse signal $x \in {\mathbb R} ^n$ that has only $k \ll n$ non-zero coefficients from a small number $m \ll n$ of linear projections. The projections are…
Recent research in tomographic reconstruction is motivated by the need to efficiently recover detailed anatomy from limited measurements. One of the ways to compensate for the increasingly sparse sets of measurements is to exploit the…
Using the techniques of [arXiv:0911.4271], upper bounds for a given confidence level are modified in an optimal fashion to incorporate the a priori information that the parameter being estimated is non-negative. A paradox with different…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a limited number of noisy linear measurements is an important problem in compressed sensing. In the high-dimensional setting, it is known that recovery with a…
Numerous quantum many-body systems are characterized by either fundamental or emergent constraints---such as gauge symmetries or parity superselection for fermions---which effectively limit the accessible observables and realizable…
The $\ell^0$ minimization of compressed sensing is often relaxed to $\ell^1$, which yields easy computation using the shrinkage mapping known as soft thresholding, and can be shown to recover the original solution under certain hypotheses.…
Compressed sensing (sparse signal recovery) has been a popular and important research topic in recent years. By observing that natural signals are often nonnegative, we propose a new framework for nonnegative signal recovery using…
Global-local shrinkage prior has been recognized as useful class of priors which can strongly shrink small signals towards prior means while keeping large signals unshrunk. Although such priors have been extensively discussed under Gaussian…
Convergence bounds are one of the main tools to obtain information on the performance of a distributed machine learning task, before running the task itself. In this work, we perform a set of experiments to assess to which extent, and in…
A simple hard-thresholding operation is shown to be able to recover $L$ signals $\mathbf{x}_1,...,\mathbf{x}_L \in \mathbb{R}^n$ that share a common support of size $s$ from $m = \mathcal{O}(s)$ one-bit measurements per signal if $L \ge…
In recent years, semidefinite relaxations of common optimization problems in robotics have attracted growing attention due to their ability to provide globally optimal solutions. In many cases, it was shown that specific handcrafted…