Related papers: A Sparse Representation of Random Signals
Sparse signals can be recovered from a reduced set of samples by using compressive sensing algorithms. In common methods the signal is recovered in the sparse domain. A method for the reconstruction of sparse signal which reconstructs the…
In this paper, we propose a time-frequency analysis method to obtain instantaneous frequencies and the corresponding decomposition by solving an optimization problem. In this optimization problem, the basis to decompose the signal is not…
In the spatial channel models used in multi-antenna wireless communications, the propagation from a single-antenna transmitter (e.g., a user) to an M-antenna receiver (e.g., a Base Station) occurs through scattering clusters located in the…
This paper proposes two coherent broadband focusing algorithms for spatial correlation estimation using sparse linear arrays. Both algorithms decompose the time-domain array data into disjoint frequency bands through discrete Fourier…
We consider the problem of recovery of an unknown multivariate signal $f$ observed in a $d$-dimensional Gaussian white noise model of intensity $\varepsilon$. We assume that $f$ belongs to a class of smooth functions ${\cal F}^d\subset…
In this paper the problem of blind super-resolution of sparse signals using arbitrary sampling scheme and atomic lift is discussed. After comprehensive description on blind superresolution problem, it is shown that using Prolate Spheroidal…
Time-frequency images (TFIs) provide a joint time-frequency representation of a signal and have become an effective tool for analyzing, characterizing, and processing non-stationary signals. Deep learning (DL) techniques have become…
Features based on sparse representation, especially using the synthesis dictionary model, have been heavily exploited in signal processing and computer vision. However, synthesis dictionary learning typically involves NP-hard sparse coding…
Generalized Fourier series with orthogonal polynomial bases have useful applications in several fields, including differential equations, pattern recognition, and image and signal processing. However, computing the generalized Fourier…
In this paper, we will generate a convex iterative FP thresholding algorithm to solve the problem $(FP^{\lambda}_{a})$. Two schemes of convex iterative FP thresholding algorithms are generated. One is convex iterative FP thresholding…
We develop an iterative, adaptive frequency sensing protocol based on Ramsey interferometry of a two-level system. Our scheme allows one to estimate unknown frequencies with a high precision from short, finite signals. It avoids several…
We study the Fourier ratio of a signal $f:\mathbb Z_N\to\mathbb C$, \[ \mathrm{FR}(f)\ :=\ \sqrt{N}\,\frac{\|\widehat f\|_{L^1(\mu)}}{\|\widehat f\|_{L^2(\mu)}} \ =\ \frac{\|\widehat f\|_1}{\|\widehat f\|_2}, \] as a simple scalar parameter…
We develop sparse array receive beamformer design methods achieving maximum signal-to-interference plus noise ratio (MaxSINR) for wideband sources and jammers. Both tapped delay line (TDL) filtering and the DFT realizations to wideband…
Sparse coding strategies have been lauded for their parsimonious representations of data that leverage low dimensional structure. However, inference of these codes typically relies on an optimization procedure with poor computational…
Dynamic Mode Decomposition (DMD) is a data based modeling tool that identifies a matrix to map a quantity at some time instant to the same quantity in future. We design a new version which we call Adaptive Dynamic Mode Decomposition (ADMD)…
Recovery of arbitrarily positioned samples that are missing in sparse signals recently attracted significant research interest. Sparse signals with heavily corrupted arbitrary positioned samples could be analyzed in the same way as…
Orthogonal time frequency space (OTFS) modulation has recently been identified as a suitable waveform for joint radar and communication systems. Focusing on the effect of data modulation on the radar sensing performance, we derive the…
Time-frequency representation (TFR) allowing for mode reconstruction plays a significant role in interpreting and analyzing the nonstationary signal constituted of various modes. However, it is difficult for most previous methods to handle…
Tensors have found application in a variety of fields, ranging from chemometrics to signal processing and beyond. In this paper, we consider the problem of multilinear modeling of sparse count data. Our goal is to develop a descriptive…
Implicit neural representations are a promising new avenue of representing general signals by learning a continuous function that, parameterized as a neural network, maps the domain of a signal to its codomain; the mapping from spatial…