Related papers: Fast Algorithms for Demixing Sparse Signals from N…
In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts to recover the phase information of a signal from the…
This paper investigates how models of spatiotemporal dynamics in the form of nonlinear partial differential equations can be identified directly from noisy data using a combination of sparse regression and weak formulation. Using the…
Line spectral estimation is the problem of recovering the frequencies and amplitudes of a mixture of a few sinusoids from equispaced samples. However, in a variety of signal processing problems arising in imaging, radar, and localization we…
Convolutional sparse coding (CSC) can learn representative shift-invariant patterns from multiple kinds of data. However, existing CSC methods can only model noises from Gaussian distribution, which is restrictive and unrealistic. In this…
Greedy Pursuits are very popular in Compressed Sensing for sparse signal recovery. Though many of the Greedy Pursuits possess elegant theoretical guarantees for performance, it is well known that their performance depends on the statistical…
We consider the well-studied problem of decomposing a vector time series signal into components with different characteristics, such as smooth, periodic, nonnegative, or sparse. We describe a simple and general framework in which the…
Sensor placement for linear inverse problems is the selection of locations to assign sensors so that the entire physical signal can be well recovered from partial observations. In this paper, we propose a fast sampling algorithm to place…
In the community of remote sensing, nonlinear mixing models have recently received particular attention in hyperspectral image processing. In this paper, we present a novel nonlinear spectral unmixing method following the recent multilinear…
In this report, a novel efficient algorithm for recovery of jointly sparse signals (sparse matrix) from multiple incomplete measurements has been presented, in particular, the NESTA-based MMV optimization method. In a nutshell, the jointly…
Hyperspectral image (HSI) denoising has been attracting much research attention in remote sensing area due to its importance in improving the HSI qualities. The existing HSI denoising methods mainly focus on specific spectral and spatial…
In many compressive sensing problems today, the relationship between the measurements and the unknowns could be nonlinear. Traditional treatment of such nonlinear relationships have been to approximate the nonlinearity via a linear model…
We study sparse signal recovery from noisy linear observations using nonconvex log-sum regularization. The log-sum penalty reduces the shrinkage bias of $\ell_1$ regularization and more closely approximates the $\ell_0$ regularization, but…
We study the question of reconstructing two signals $f$ and $g$ from their convolution $y = f\ast g$. This problem, known as {\em blind deconvolution}, pervades many areas of science and technology, including astronomy, medical imaging,…
The development of signal unmixing algorithms is essential for leveraging multimodal datasets acquired through a wide array of scientific imaging technologies, including hyperspectral or time-resolved acquisitions. In experimental physics,…
This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…
Modeling real-world systems requires accounting for noise - whether it arises from unpredictable fluctuations in financial markets, irregular rhythms in biological systems, or environmental variability in ecosystems. While the behavior of…
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.…
Wideband analog signals push contemporary analog-to-digital conversion systems to their performance limits. In many applications, however, sampling at the Nyquist rate is inefficient because the signals of interest contain only a small…
Recently, the problem of blind image separation has been widely investigated, especially the medical image denoise which is the main step in medical diag-nosis. Removing the noise without affecting relevant features of the image is the main…
This paper investigates the recovery of a node-domain sparse graph signal from the output of a graph filter. This problem, which is often referred to as the identification of the source of a diffused sparse graph signal, is seminal in the…