Related papers: Compressed Sensing Matrices from Fourier Matrices
We present a general class of compressed sensing matrices which are then demonstrated to have associated sublinear-time sparse approximation algorithms. We then develop methods for constructing specialized matrices from this class which are…
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. This paper studies a $K \times N$ partial Fourier measurement matrix for compressed sensing which is deterministically…
In this paper, a class of deterministic sensing matrices are constructed by selecting rows from Fourier matrices. These matrices have better performance in sparse recovery than random partial Fourier matrices. The coherence and restricted…
In this paper, a new class of circulant matrices built from deterministic sequences is proposed for convolution-based compressed sensing (CS). In contrast to random convolution, the coefficients of the underlying filter are given by the…
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this correspondence, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via additive…
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this paper, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via multiplicative…
The primary goal of this work is to review the importance of data compression and present a fast Fourier-based method for generating the deterministic compression matrix in the area of deterministic compressed sensing. The principle…
Compressed sensing (CS) is a signal acquisition paradigm to simultaneously acquire and reduce dimension of signals that admit sparse representation. This is achieved by collecting linear, non-adaptive measurements of a signal, which can be…
Recent development in compressed sensing (CS) has revealed that the use of a special design of measurement matrix, namely the spatially-coupled matrix, can achieve the information-theoretic limit of CS. In this paper, we consider the…
In 'An asymptotic result on compressed sensing matrices', a new construction for compressed sensing matrices using combinatorial design theory was introduced. In this paper, we use deterministic and probabilistic methods to analyse the…
In its most elementary form, compressed sensing studies the design of decoding algorithms to recover a sufficiently sparse vector or code from a lower dimensional linear measurement vector. Typically it is assumed that the decoder has…
Compressed sensing (CS) enables people to acquire the compressed measurements directly and recover sparse or compressible signals faithfully even when the sampling rate is much lower than the Nyquist rate. However, the pure random sensing…
Compressed sensing (CS) is a sampling theory that allows reconstruction of sparse (or compressible) signals from an incomplete number of measurements, using of a sensing mechanism implemented by an appropriate projection matrix. The CS…
We provide the first analysis of a non-trivial quantization scheme for compressed sensing measurements arising from structured measurements. Specifically, our analysis studies compressed sensing matrices consisting of rows selected at…
In Compressed Sensing the matrices that satisfy the Restricted Isometry Property (RIP) play an important role. But to date, very few results for designing such matrices are available. For applications such as multiplier-less data…
This note complements the paper "The quest for optimal sampling: Computationally efficient, structure-exploiting measurements for compressed sensing" [2]. Its purpose is to present a proof of a result stated therein concerning the recovery…
Compressed sensing is a signal processing technique whereby the limits imposed by the Shannon--Nyquist theorem can be exceeded provided certain conditions are imposed on the signal. Such conditions occur in many real-world scenarios, and…
We look at the use of deterministic sensing matrices for compressed sensing and provide worst-case bounds on the classification accuracy of SVMs on compressively sensed data.
We consider the compressive sensing of a sparse or compressible signal ${\bf x} \in {\mathbb R}^M$. We explicitly construct a class of measurement matrices, referred to as the low density frames, and develop decoding algorithms that produce…
This paper deals with the design of a sensing matrix along with a sparse recovery algorithm by utilizing the probability-based prior information for compressed sensing system. With the knowledge of the probability for each atom of the…