Related papers: Transient Performance Analysis of the $\ell_1$-RLS
Distributed adaptive signal processing has attracted much attention in the recent decade owing to its effectiveness in many decentralized real-time applications in networked systems. Because many natural signals are highly sparse with most…
In this paper we revisit one of the classical problems of compressed sensing. Namely, we consider linear under-determined systems with sparse solutions. A substantial success in mathematical characterization of an $\ell_1$ optimization…
There is a recent surge of interest in developing algorithms for finding sparse solutions of underdetermined systems of linear equations $y = \Phi x$. In many applications, extremely large problem sizes are envisioned, with at least tens of…
We consider the problem of recursively and causally reconstructing time sequences of sparse signals (with unknown and time-varying sparsity patterns) from a limited number of noisy linear measurements. The sparsity pattern is assumed to…
Recently, tensor data (or multidimensional array) have been generated in many modern applications, such as functional magnetic resonance imaging (fMRI) in neuroscience and videos in video analysis. Many efforts are made in recent years to…
Broadband frequency-selective fading channels usually have the inherent sparse nature. By exploiting the sparsity, adaptive sparse channel estimation (ASCE) algorithms, e.g., least mean square with reweighted L1-norm constraint (LMS-RL1)…
We present a new algorithm and the corresponding convergence analysis for the regularization of linear inverse problems with sparsity constraints, applied to a new generalized sparsity promoting functional. The algorithm is based on the…
Least mean square (LMS) type adaptive algorithms have attracted much attention due to their low computational complexity. In the scenarios of sparse channel estimation, zero-attracting LMS (ZA-LMS), reweighted ZA-LMS (RZA-LMS) and…
We consider the problem of learning a sparse graph under the Laplacian constrained Gaussian graphical models. This problem can be formulated as a penalized maximum likelihood estimation of the Laplacian constrained precision matrix. Like in…
Conventional algorithms for sparse signal recovery and sparse representation rely on $l_1$-norm regularized variational methods. However, when applied to the reconstruction of $\textit{sparse images}$, i.e., images where only a few pixels…
We study the problem of learning a sparse linear regression vector under additional conditions on the structure of its sparsity pattern. This problem is relevant in machine learning, statistics and signal processing. It is well known that a…
An evolving line of machine learning works observe empirical evidence that suggests interpolating estimators -- the ones that achieve zero training error -- may not necessarily be harmful. This paper pursues theoretical understanding for an…
We study the robustness properties of $\ell_1$ norm minimization for the classical linear regression problem with a given design matrix and contamination restricted to the dependent variable. We perform a fine error analysis of the $\ell_1$…
Most detection algorithms in spatial modulation (SM) are formulated as linear regression via the regularized least-squares (RLS) method. In this method, the transmit signal is estimated by minimizing the residual sum of squares penalized…
Noise problems in signals have gained huge attention due to the need of noise-free output signal in numerous communication systems. The principal of adaptive noise cancellation is to acquire an estimation of the unwanted interfering signal…
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. While naturally cast as a combinatorial optimization problem, variable or feature selection admits a convex relaxation through the…
The Broad Learning System (BLS) has gained significant attention for its computational efficiency and less network parameters compared to deep learning structures. However, the standard BLS relies on the pseudoinverse solution, which…
Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…
The proportionate normalized least mean square (PNLMS) algorithm and its variants are by far the most popular adaptive filters that are used to identify sparse systems. The convergence speed of the PNLMS algorithm, though very high…
Recently, in a series of papers [32,38,39,41], the ratio of $\ell_1$ and $\ell_2$ norms was proposed as a sparsity inducing function for noiseless compressed sensing. In this paper, we further study properties of such model in the noiseless…