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Dynamic mode decomposition (DMD) provides a practical means of extracting insightful dynamical information from fluids datasets. Like any data processing technique, DMD's usefulness is limited by its ability to extract real and accurate…
Finding the sparse representation of a signal in an overcomplete dictionary has attracted a lot of attention over the past years. This paper studies ProSparse, a new polynomial complexity algorithm that solves the sparse representation…
For the additive white Gaussian noise channel with average codeword power constraint, sparse superposition codes are developed. These codes are based on the statistical high-dimensional regression framework. The paper [IEEE Trans. Inform.…
In this paper, we present a new image segmentation method based on the concept of sparse subset selection. Starting with an over-segmentation, we adopt local spectral histogram features to encode the visual information of the small segments…
The 3-D total variation (3DTV) is a powerful regularization term, which encodes the local smoothness prior structure underlying a hyper-spectral image (HSI), for general HSI processing tasks. This term is calculated by assuming identical…
This paper presents a variational based approach to fusing hyperspectral and multispectral images. The fusion process is formulated as an inverse problem whose solution is the target image assumed to live in a much lower dimensional…
One-dimensional signal decomposition is a well-established and widely used technique across various scientific fields. It serves as a highly valuable pre-processing step for data analysis. While traditional decomposition techniques often…
In this letter, we propose a novel image denoising method based on correlation preserving sparse coding. Because the instable and unreliable correlations among basis set can limit the performance of the dictionary-driven denoising methods,…
The dictionary-aided sparse regression (SR) approach has recently emerged as a promising alternative to hyperspectral unmixing (HU) in remote sensing. By using an available spectral library as a dictionary, the SR approach identifies the…
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…
We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of…
We propose a new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements…
The power of sparse signal coding with learned dictionaries has been demonstrated in a variety of applications and fields, from signal processing to statistical inference and machine learning. However, the statistical properties of these…
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…
Remote sensing image super-resolution (SR) is a crucial task to restore high-resolution (HR) images from low-resolution (LR) observations. Recently, the Denoising Diffusion Probabilistic Model (DDPM) has shown promising performance in image…
Sparse representation with respect to an overcomplete dictionary is often used when regularizing inverse problems in signal and image processing. In recent years, the Convolutional Sparse Coding (CSC) model, in which the dictionary consists…
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…
Convolutional Sparse Coding (CSC) is a well-established image representation model especially suited for image restoration tasks. In this work, we extend the applicability of this model by proposing a supervised approach to convolutional…
Sparse coding is a class of unsupervised methods for learning a sparse representation of the input data in the form of a linear combination of a dictionary and a sparse code. This learning framework has led to state-of-the-art results in…
Conventional compressed sensing theory assumes signals have sparse representations in a known, finite dictionary. Nevertheless, in many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the…