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Sparse Bayesian learning (SBL) is a popular approach to sparse signal recovery in compressed sensing (CS). In SBL, the signal sparsity information is exploited by assuming a sparsity-inducing prior for the signal that is then estimated…
This paper presents a sparse Bayesian learning algorithm for inverse problems in signal and image processing with a total variation (TV) sparsity prior. Because of the prior used, and the fact that the prior parameters are estimated…
Sparse Bayesian learning (SBL) has emerged as a fast and competitive method to perform sparse processing. The SBL algorithm, which is developed using a Bayesian framework, approximately solves a non-convex optimization problem using fixed…
Block-sparse signal recovery without knowledge of block sizes and boundaries, such as those encountered in multi-antenna mmWave channel models, is a hard problem for compressed sensing (CS) algorithms. We propose a novel Sparse Bayesian…
This paper introduces a new sparse Bayesian learning (SBL) algorithm that jointly recovers a temporal sequence of edge maps from noisy and under-sampled Fourier data. The new method is cast in a Bayesian framework and uses a prior that…
Block sparsity is a widely exploited structure in sparse recovery, offering significant gains when signal blocks are known. Yet, practical signals often exhibit unknown block boundaries and isolated non-zero entries, which challenge…
Sparse Bayesian learning (SBL) is a powerful framework for tackling the sparse coding problem. However, the most popular inference algorithms for SBL become too expensive for high-dimensional settings, due to the need to store and compute a…
We address the recovery of sparse vectors in an overcomplete, linear and noisy multiple measurement framework, where the measurement matrix is known upto a permutation of its rows. We derive sparse Bayesian learning (SBL) based updates for…
Sparse Bayesian Learning (SBL) models are extensively used in signal processing and machine learning for promoting sparsity through hierarchical priors. The hyperparameters in SBL models are crucial for the model's performance, but they are…
We address the sparse signal recovery problem in the context of multiple measurement vectors (MMV) when elements in each nonzero row of the solution matrix are temporally correlated. Existing algorithms do not consider such temporal…
This work addresses the fundamental linear inverse problem in compressive sensing (CS) by introducing a new type of regularizing generative prior. Our proposed method utilizes ideas from classical dictionary-based CS and, in particular,…
Due to its self-regularizing nature and its ability to quantify uncertainty, the Bayesian approach has achieved excellent recovery performance across a wide range of sparse signal recovery applications. However, most existing methods are…
This study addresses the problem of discrete signal reconstruction from the perspective of sparse Bayesian learning (SBL). Generally, it is intractable to perform the Bayesian inference with the ideal discretization prior under the SBL…
Sparse signal recovery algorithms like sparse Bayesian learning work well but the complexity quickly grows when tackling higher dimensional parametric dictionaries. In this work we propose a novel Bayesian strategy to address the two…
Sparse Bayesian Learning (SBL) is a powerful framework for attaining sparsity in probabilistic models. Herein, we propose a coordinate ascent algorithm for SBL termed Relevance Matching Pursuit (RMP) and show that, as its noise variance…
The recovery of block-sparse signals with unknown structural patterns remains a fundamental challenge in structured sparse signal reconstruction. By proposing a variance transformation framework, this paper unifies existing pattern-based…
Many signal processing applications require estimation of time-varying sparse signals, potentially with the knowledge of an imperfect dynamics model. In this paper, we propose an algorithm for dynamic filtering of time-varying sparse…
In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the…
Accurate channel estimation is a key requirement in extremely large-scale multiple-input multiple-output (XL-MIMO) systems. Sparse Bayesian learning (SBL) is a well-established framework for exploiting channel sparsity, but its performance…
Sparse Bayesian Learning (SBL) constructs an extremely sparse probabilistic model with very competitive generalization. However, SBL needs to invert a big covariance matrix with complexity $O(M^3)$ (M: feature size) for updating the…