Related papers: A Sparse Representation of Random Signals
Time-frequency analysis has been applied successfully in many fields. However, the traditional methods, like short time Fourier transform and Cohen distribution, suffer from the low resolution or the interference of the cross terms. To…
Even though image signals are typically defined on a regular two-dimensional grid, there also exist many scenarios where this is not the case and the amplitude of the image signal only is available for a non-regular subset of pixel…
Signal modeling lies at the core of numerous signal and image processing applications. A recent approach that has drawn considerable attention is sparse representation modeling, in which the signal is assumed to be generated as a…
This paper provides a fundamental characterization of the discrete ambiguity functions (AFs) of random communication waveforms under arbitrary orthonormal modulation with random constellation symbols, which serve as a key metric for…
In this paper we study the compressive sensing effects on 2D signals exhibiting sparsity in 2D DFT domain. A simple algorithm for reconstruction of randomly under-sampled data is proposed. It is based on the analytically determined…
In this paper, a novel and robust algorithm is proposed for adaptive beamforming based on the idea of reconstructing the autocorrelation sequence (ACS) of a random process from a set of measured data. This is obtained from the first column…
In this paper, adaptive non-uniform compressive sampling (ANCS) of time-varying signals, which are sparse in a proper basis, is introduced. ANCS employs the measurements of previous time steps to distribute the sensing energy among…
Sparse Representation (SR) of signals or data has a well founded theory with rigorous mathematical error bounds and proofs. SR of a signal is given by superposition of very few columns of a matrix called Dictionary, implicitly reducing…
Fourier representation (FR) is an indispensable mathematical formulation for modeling and analysis of physical phenomenon, engineering systems and signals in numerous applications. In this study, we present the generalized Fourier…
In this paper, we consider a fractional Poisson random field (FPRF) on positive plane. It is defined as a process whose one dimensional distribution is the solution of a system of fractional partial differential equations. A time-changed…
Despite the importance of sparsity signal models and the increasing prevalence of high-dimensional streaming data, there are relatively few algorithms for dynamic filtering of time-varying sparse signals. Of the existing algorithms, fewer…
We propose a novel estimation approach for the covariance matrix based on the $l_1$-regularized approximate factor model. Our sparse approximate factor (SAF) covariance estimator allows for the existence of weak factors and hence relaxes…
Recently, a number of mostly $\ell_1$-norm regularized least squares type deterministic algorithms have been proposed to address the problem of \emph{sparse} adaptive signal estimation and system identification. From a Bayesian perspective,…
Multivariate regression techniques are commonly applied to explore the associations between large numbers of outcomes and predictors. In real-world applications, the outcomes are often of mixed types, including continuous measurements,…
Analog signal processing (ASP) is presented as a systematic approach to address future challenges in high speed and high frequency microwave applications. The general concept of ASP is explained with the help of examples emphasizing basic…
We investigate the recovery of signals exhibiting a sparse representation in a general (i.e., possibly redundant or incomplete) dictionary that are corrupted by additive noise admitting a sparse representation in another general dictionary.…
Sampling theories lie at the heart of signal processing devices and communication systems. To accommodate high operating rates while retaining low computational cost, efficient analog-to digital (ADC) converters must be developed. Many of…
This paper proposes a sparse regression method that continuously interpolates between Forward Stepwise selection (FS) and the LASSO. When tuned appropriately, our solutions are much sparser than typical LASSO fits but, unlike FS fits,…
Many signal processing applications such as acoustic echo cancellation and wireless channel estimation require identifying systems where only a small fraction of coefficients are actually active, i.e. sparse systems. Zero-attracting…
Some elements of the theory and algorithmics corresponding to the computation of semilinear sparse models for discrete-time signals are presented. In this study, we will focus on approximately eventually periodic discrete-time signals, that…