Compressive Sensing (CS) theory breaks through the limitations of traditional Nyquist sampling theorem, accomplishes the compressive sampling and reconstruction of signals based on sparsity or compressibility. In this paper CS is presented in a Bayesian framework for linear frequency modulated (LFM) cases whose likelihood or priors are usually Gaussian. In order to decrease the sampling pressur...

We consider in this paper the problem of reconstructing block-sparse signals with unknown block partitions. In the first part of this work, we extend the block-sparse Bayesian learning (BSBL) originally developed for recovering a single block-sparse signal in a single compressive sensing (CS) task scenario to the case of multiple CS tasks. A newmulti-task signal recovery algorithm, called the e...

This paper provides a compressive sensing (CS) method of denoising images using Bayesian framework. Some images, for example like magnetic resonance images (MRI) are usually very weak due to the presence of noise and due to the weak nature of the signal itself. So denoising boosts the true signal strength. Under Bayesian framework, we have used two different priors: sparsity and clusterdness in...

Compressive sensing (CS) is an emerging field that, under appropriate conditions, can significantly reduce the number of measurements required for a given signal. Specifically, if the m-dimensional signal u is sparse in an orthonormal basis represented by the m × m matrix Ψ, then one may infer u based on n m projection measurements. If u = Ψθ, where θ are the sparse coefficients in basis Ψ, the...

A key problem in statistics and machine learning is inferring suitable structure of a model given some observed data. A Bayesian approach to model comparison makes use of the marginal likelihood of each candidate model to form a posterior distribution over models; unfortunately for most models of interest, notably those containing hidden or latent variables, the marginal likelihood is intractab...

Compressive Sensing (CS) provides a new paradigm of sub-Nyquist sampling which can be considered as an alternative to Nyquist sampling theorem. In particular, providing that signals are with sparse representations in some known space (or domain), information can be perfectly preserved even with small amount of measurements captured by random projections. Besides sparsity prior of signals, the i...

A Pavlovian conditioned stimulus (CS) associated with a reward can enhance an instrumental response directed to the same or other rewards. This effect is called Pavlovian-instrumental transfer (PIT). In recent years, lesion studies using rats have gained insight into its neural substrates dissociating between specific PIT (where CS and instrumental response share the same reward) and general PI...

Abstract—This paper provides clustered compressive sensing (CCS) based image processing using Bayesian framework applied to medical images. Some images, for example like magnetic resonance images (MRI) are usually very weak due to the presence of noise and due to the weak nature of the signal itself. Compressed sensing (CS) paradigm can be applied in order to boost such signals. We applied CS p...

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 using Bayesian inference. In this paper, a new sparsity-inducing prior is introduced and efficient algorithms are developed for signal recovery. The main algorit...