Related papers: On the Global-Local Dichotomy in Sparsity Modeling
We present a novel sparsity-based space-time adaptive processing (STAP) technique based on the alternating direction method to overcome the severe performance degradation caused by array gain/phase (GP) errors. The proposed algorithm…
A major challenge for building statistical models in the big data era is that the available data volume far exceeds the computational capability. A common approach for solving this problem is to employ a subsampled dataset that can be…
Inexact alternating direction multiplier methods (ADMMs) are developed for solving general separable convex optimization problems with a linear constraint and with an objective that is the sum of smooth and nonsmooth terms. The approach…
The non-negative solution to an underdetermined linear system can be uniquely recovered sometimes, even without imposing any additional sparsity constraints. In this paper, we derive conditions under which a unique non-negative solution for…
Traditional patch-based sparse representation modeling of natural images usually suffer from two problems. First, it has to solve a large-scale optimization problem with high computational complexity in dictionary learning. Second, each…
The iterations of many sparse estimation algorithms are comprised of a fixed linear filter cascaded with a thresholding nonlinearity, which collectively resemble a typical neural network layer. Consequently, a lengthy sequence of algorithm…
Sparse signal recovery problems from noisy linear measurements appear in many areas of wireless communications. In recent years, deep learning (DL) based approaches have attracted interests of researchers to solve the sparse linear inverse…
Inverse source localization from Helmholtz boundary data collected over a narrow aperture is highly ill-posed and severely undersampled, undermining classical solvers (e.g., the Direct Sampling Method). We present a modular framework that…
With the availability of extraordinarily huge data sets, solving the problems of distributed statistical methodology and computing for such data sets has become increasingly crucial in the big data area. In this paper, we focus on the…
Generative graph models struggle to scale due to the need to predict the existence or type of edges between all node pairs. To address the resulting quadratic complexity, existing scalable models often impose restrictive assumptions such as…
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…
Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…
As we aim at alleviating the curse of high-dimensionality, subspace learning is becoming more popular. Existing approaches use either information about global or local structure of the data, and few studies simultaneously focus on global…
Natural signals and images are well-known to be approximately sparse in transform domains such as Wavelets and DCT. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing…
Many applications like audio and image processing show that sparse representations are a powerful and efficient signal modeling technique. Finding an optimal dictionary that generates at the same time the sparsest representations of data…
State-of-the-art subspace clustering methods are based on self-expressive model, which represents each data point as a linear combination of other data points. By enforcing such representation to be sparse, sparse subspace clustering is…
In this paper, we propose a novel distributed algorithm for consensus optimization over networks and a robust extension tailored to deal with asynchronous agents and packet losses. Indeed, to robustly achieve dynamic consensus on the…
We study an ill-posed linear inverse problem, where a binary sequence will be reproduced using a sparce matrix. According to the previous study, this model can theoretically provide an optimal compression scheme for an arbitrary distortion…
Accurately reconstructing a global spatial field from sparse data has been a longstanding problem in several domains, such as Earth Sciences and Fluid Dynamics. Historically, scientists have approached this problem by employing complex…
We consider the problem of learning a graph modeling the statistical relations of the $d$ variables from a dataset with $n$ samples $X \in \mathbb{R}^{n \times d}$. Standard approaches amount to searching for a precision matrix $\Theta$…