Abstract
In multi-task compressive sensing (MCS), the original signals of multiple compressive sensing (CS) tasks are assumed to be correlated. This is explored to recover signals in a joint manner to improve signal reconstruction performance. In this paper, we first develop an improved version of MCS that imposes sparseness over the original signals using Laplace priors. The newly proposed technique, termed as the Laplace prior-based MCS (LMCS), adopts a hierarchical prior model, and the MCS is shown analytically to be a special case of LMCS. This paper next considers the scenario where the CS tasks belong to different groups. In this case, the original signals from different task groups are not well correlated, which would degrade the signal recovery performance of both MCS and LMCS. We propose the use of the minimum description length (MDL) principle to enhance the MCS and LMCS techniques. New algorithms, referred to as MDL-MCS and MDL-LMCS, are developed. They first classify tasks into different groups and then reconstruct signals from each cluster jointly. Simulations demonstrate that the proposed algorithms have better performance over several state-of-art benchmark techniques.
Highlights
If a signal is compressible in the sense that its representation in a certain linear canonical basis is sparse, it can be recovered from measurements obtained at a rate much lower than the Nyquist frequency using the technique of compressive sensing (CS) [1,2,3]
The results show that in both cases, the reconstruction error of Laplace prior-based MCS (LMCS) gradually improves as the number of compressive measurements increases, and the best performance is obtained when λ is estimated using Equation 25
For the purpose of comparison, we show the results of the ST-Bayesian compressive sensing (BCS), LST-BCS, multi-task compressive sensing (MCS), and LMCS methods as well as the DP-MCS technique
Summary
If a signal is compressible in the sense that its representation in a certain linear canonical basis is sparse, it can be recovered from measurements obtained at a rate much lower than the Nyquist frequency using the technique of compressive sensing (CS) [1,2,3]. In order to provide satisfactory signal reconstruction performance, the MCS technique from [7], together with the newly proposed LMCS method, requires that the original signals of the multiple CS tasks are well correlated statistically. This assumption may not be fulfilled in many practical applications. Inference and could suffer from local convergence, the newly proposed MDL-MCS and MDL-LMCS methods offer improved correct signal classification rate and better signal reconstruction performance The original signals θ i are reconstructed using the estimated values of α and β
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