Related papers: Deterministic Designs with Deterministic Guarantee…
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…
Recent work in compressed sensing theory shows that $n\times N$ independent and identically distributed (IID) sensing matrices whose entries are drawn independently from certain probability distributions guarantee exact recovery of a sparse…
Compressed Sensing aims to capture attributes of $k$-sparse signals using very few measurements. In the standard Compressed Sensing paradigm, the $\m\times \n$ measurement matrix $\A$ is required to act as a near isometry on the set of all…
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…
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…
How to construct a suitable measurement matrix is still an open question in compressed sensing. A significant part of the recent work is that the measurement matrices are not completely random on the entries but exhibit considerable…
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…
The expicit restricted isometry property (RIP) measurement matrices are needed in practical application of compressed sensing in signal processing. RIP matrices from Reed-Solomon codes, BCH codes, orthogonal codes, expander graphs have been…
Consider the ensemble of real symmetric Toeplitz matrices, each independent entry an i.i.d. random variable chosen from a fixed probability distribution p of mean 0, variance 1, and finite higher moments. Previous investigations showed that…
The restricted isometry property (RIP) is a well-known matrix condition that provides state-of-the-art reconstruction guarantees for compressed sensing. While random matrices are known to satisfy this property with high probability,…
This paper considers compressed sensing matrices and neighborliness of a centrally symmetric convex polytope generated by vectors $\pm X_1,...,\pm X_N\in\R^n$, ($N\ge n$). We introduce a class of random sampling matrices and show that they…
We investigate the joint convergence of independent random Toeplitz matrices with complex input entries that have a pair-correlation structure, along with deterministic Toeplitz matrices and the backward identity permutation matrix.…
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…
Recently, the statistical restricted isometry property (RIP) has been formulated to analyze the performance of deterministic sampling matrices for compressed sensing. In this paper, we propose the usage of orthogonal symmetric Toeplitz…
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…
Discrete-time domain Iterative Learning Control (ILC) schemes inspired by Repetitive control algorithms are proposed and analyzed. The well known relation between a discrete-time plant (filter) and its Markov Toeplitz matrix representation…
Compressed sensing seeks to recover a sparse vector from a small number of linear and non-adaptive measurements. While most work so far focuses on Gaussian or Bernoulli random measurements we investigate the use of partial random circulant…
A new nonparametric approach for system identification has been recently proposed where the impulse response is modeled as the realization of a zero-mean Gaussian process whose covariance (kernel) has to be estimated from data. In this…
In this paper, deterministic construction of measurement matrices in Compressive Sensing (CS) is considered. First, by employing the column replacement concept, a theorem for construction of large minimum distance linear codes containing…
Superregular matrices are a class of lower triangular Toeplitz matrices that arise in the context of constructing convolutional codes having a maximum distance profile. These matrices are characterized by the property that no submatrix has…