Related papers: One Bit to Rule Them All : Binarizing the Reconstr…
We introduce q-ary compressive sensing, an extension of 1-bit compressive sensing. We propose a novel sensing mechanism and a corresponding recovery procedure. The recovery properties of the proposed approach are analyzed both theoretically…
The recovery of signals with finite-valued components from few linear measurements is a problem with widespread applications and interesting mathematical characteristics. In the compressed sensing framework, tailored methods have been…
Signals sparse in a transformation domain can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Simple re- construction algorithms are presented in the first part of the paper. The…
One-bit compressive sensing gains its popularity in signal processing and communications due to its low storage costs and low hardware complexity. However, it has been a challenging task to recover the signal only by exploiting the one-bit…
The goal of standard 1-bit compressive sensing is to accurately recover an unknown sparse vector from binary-valued measurements, each indicating the sign of a linear function of the vector. Motivated by recent advances in compressive…
Parameterized mathematical models play a central role in understanding and design of complex information systems. However, they often cannot take into account the intricate interactions innate to such systems. On the contrary, purely…
In this paper, we study the problem of compressed sensing using binary measurement matrices and $\ell_1$-norm minimization (basis pursuit) as the recovery algorithm. We derive new upper and lower bounds on the number of measurements to…
The one-bit compressed sensing framework aims to reconstruct a sparse signal by only using the sign information of its linear measurements. To compensate for the loss of scale information, past studies in the area have proposed recovering…
We present a Compressive Sensing algorithm for reconstructing binary signals from its linear measurements. The proposed algorithm minimizes a non-convex cost function expressed as a weighted sum of smoothed $\ell_0$ norms which takes into…
The article concerns compressed sensing methods in the quaternion algebra. We prove that it is possible to uniquely reconstruct - by $\ell_1$ norm minimization - a sparse quaternion signal from a limited number of its real linear…
We consider the problem of sparse signal recovery from 1-bit measurements. Due to the noise present in the acquisition and transmission process, some quantized bits may be flipped to their opposite states. These sign flips may result in…
Compressive sensing is a methodology for the reconstruction of sparse or compressible signals using far fewer samples than required by the Nyquist criterion. However, many of the results in compressive sensing concern random sampling…
This work treats the recovery of sparse, binary signals through box-constrained basis pursuit using biased measurement matrices. Using a probabilistic model, we provide conditions under which the recovery of both sparse and saturated binary…
This paper formulates and studies a general distributed field reconstruction problem using a dense network of noisy one-bit randomized scalar quantizers in the presence of additive observation noise of unknown distribution. A constructive…
Compressive sensing is a technique to sample signals well below the Nyquist rate using linear measurement operators. In this paper we present an algorithm for signal reconstruction given such a set of measurements. This algorithm…
An l0-regularized linear regression for a sparse signal reconstruction is implemented based on the quadratic unconstrained binary optimization (QUBO) formulation. In this method, the signal values are quantized and expressed as bit…
Compressive sensing aims to recover a high-dimensional sparse signal from a relatively small number of measurements. In this paper, a novel design of the measurement matrix is proposed. The design is inspired by the construction of…
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…
This study presents a noise-robust framework for 1-bit diffraction tomography, a novel imaging approach that relies on intensity-only binary measurements obtained through coded apertures. The proposed reconstruction scheme leverages random…
Recent advances in unsupervised learning have highlighted the possibility of learning to reconstruct signals from noisy and incomplete linear measurements alone. These methods play a key role in medical and scientific imaging and sensing,…