Related papers: Structured LISTA for Multidimensional Harmonic Ret…
Learned Iterative Shrinkage-Thresholding Algorithm (LISTA) introduces the concept of unrolling an iterative algorithm and training it like a neural network. It has had great success on sparse recovery. In this paper, we show that adding…
Recent theory of mapping an image into a structured low-rank Toeplitz or Hankel matrix has become an effective method to restore images. In this paper, we introduce a generalized structured low-rank algorithm to recover images from their…
As a typical signal processing problem, multidimensional harmonic retrieval (MHR) has been adapted to a wide range of applications in signal processing. Block-sparse signals, whose nonzero entries appearing in clusters, have received much…
This paper presents Toeplitz-Hermitian ADMM-Net (THADMM-Net), a deep neural network obtained by deep unfolding the alternating direction method of multipliers (ADMM) algorithm for solving the least absolute shrinkage thresholding operator…
This paper studies two structured approximation problems: (1) Recovering a corrupted low-rank Toeplitz matrix and (2) recovering the range of a Fourier matrix from a single observation. Both problems are computationally challenging because…
It is well-established that many iterative sparse reconstruction algorithms can be unrolled to yield a learnable neural network for improved empirical performance. A prime example is learned ISTA (LISTA) where weights, step sizes and…
We introduce an adaptive structured low rank algorithm to recover MR images from their undersampled Fourier coefficients. The image is modeled as a combination of a piecewise constant component and a piecewise linear component. The Fourier…
Covariance matrices of noisy multichannel electroencephalogram time series data are hard to estimate due to high dimensionality. In brain-computer interfaces (BCI) based on event-related potentials and a linear discriminant analysis (LDA)…
In this paper, we propose an efficient numerical scheme for solving some large scale ill-posed linear inverse problems arising from image restoration. In order to accelerate the computation, two different hidden structures are exploited.…
Deep neural networks based on unrolled iterative algorithms have achieved remarkable success in sparse reconstruction applications, such as synthetic aperture radar (SAR) tomographic inversion (TomoSAR). However, the currently available…
Recently, the study on learned iterative shrinkage thresholding algorithm (LISTA) has attracted increasing attentions. A large number of experiments as well as some theories have proved the high efficiency of LISTA for solving sparse coding…
Solving inverse problems with iterative algorithms is popular, especially for large data. Due to time constraints, the number of possible iterations is usually limited, potentially affecting the achievable accuracy. Given an error one is…
We propose a new Iteratively Reweighted Least Squares (IRLS) algorithm for the problem of completing or denoising low-rank matrices that are structured, e.g., that possess a Hankel, Toeplitz or block-Hankel/Toeplitz structure. The algorithm…
The problems of uniform linear array (with uniform mutual coupling) calibration and Toeplitz covariance matrix estimation are re-examined for application in the receive arrays of modern High Frequency Over-the-Horizon Radars (HF OTHR).…
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…
The idea of unfolding iterative algorithms as deep neural networks has been widely applied in solving sparse coding problems, providing both solid theoretical analysis in convergence rate and superior empirical performance. However, for…
Motivated by the learned iterative soft thresholding algorithm (LISTA), we introduce a general class of neural networks suitable for sparse reconstruction from few linear measurements. By allowing a wide range of degrees of weight-sharing…
We introduce a learning-based algorithm to obtain a measurement matrix for compressive sensing related recovery problems. The focus lies on matrices with a constant modulus constraint which typically represent a network of analog phase…
Motivated by applications in single-cell biology and metagenomics, we investigate the problem of matrix reordering based on a noisy disordered monotone Toeplitz matrix model. We establish the fundamental statistical limit for this problem…
This paper considers the problem of robustly estimating a structured covariance matrix with an elliptical underlying distribution with known mean. In applications where the covariance matrix naturally possesses a certain structure, taking…