Learned Block Iterative Shrinkage Thresholding Algorithm for Photothermal Super Resolution Imaging.

Block-sparse regularization is already well known in active thermal imaging and is used for multiple-measurement-based inverse problems. The main bottleneck of this method is the choice of regularization parameters which differs for each experiment. We show the benefits of using a learned block iterative shrinkage thresholding algorithm (LBISTA) that is able to learn the choice of regularization parameters, without the need to manually select them. In addition, LBISTA enables the determination of a suitable weight matrix to solve the underlying inverse problem. Therefore, in this paper we present LBISTA and compare it with state-of-the-art block iterative shrinkage thresholding using synthetically generated and experimental test data from active thermography for defect reconstruction. Our results show that the use of the learned block-sparse optimization approach provides smaller normalized mean square errors for a small fixed number of iterations. Thus, this allows us to improve the convergence speed and only needs a few iterations to generate accurate defect reconstruction in photothermal super-resolution imaging.

Block sparsity-based joint compressed sensing recovery of multi-channel ECG signals.

In recent years, compressed sensing (CS) has emerged as an effective alternative to conventional wavelet based data compression techniques. This is due to its simple and energy-efficient data reduction procedure, which makes it suitable for resource-constrained wireless body area network (WBAN)-enabled electrocardiogram (ECG) telemonitoring applications. Both spatial and temporal correlations exist simultaneously in multi-channel ECG (MECG) signals. Exploitation of both types of correlations is very important in CS-based ECG telemonitoring systems for better performance. However, most of the existing CS-based works exploit either of the correlations, which results in a suboptimal performance. In this work, within a CS framework, the authors propose to exploit both types of correlations simultaneously using a sparse Bayesian learning-based approach. A spatiotemporal sparse model is employed for joint compression/reconstruction of MECG signals. Discrete wavelets transform domain block sparsity of MECG signals is exploited for simultaneous reconstruction of all the channels. Performance evaluations using Physikalisch-Technische Bundesanstalt MECG diagnostic database show a significant gain in the diagnostic reconstruction quality of the MECG signals compared with the state-of-the art techniques at reduced number of measurements. Low measurement requirement may lead to significant savings in the energy-cost of the existing CS-based WBAN systems.

ON THE BLOCK-SPARSITY OF MULTIPLE-MEASUREMENT VECTORS.

Based on the compressive sensing (CS) theory, it is possible to recover signals, which are either compressible or sparse under some suitable basis, via a small number of non-adaptive linear measurements. In this paper, we investigate recovering of block-sparse signals via multiple measurement vectors (MMVs) in the presence of noise. In this case, we consider one of the existing algorithms which provides a satisfactory estimate in terms of minimum mean-squared error but a non-sparse solution. Here, the algorithm is first modified to result in sparse solutions. Then, further modification is performed to account for the unknown block sparsity structure in the solution, as well. The performance of the proposed algorithm is demonstrated by experimental simulations and comparisons with some other algorithms for the sparse recovery problem.

MR image reconstruction with block sparsity and iterative support detection.

This work aims to develop a novel magnetic resonance (MR) image reconstruction approach motivated by the recently proposed sampling framework with union-of-subspaces model (SUoS). Based on SUoS, we propose a mathematical formalism that effectively integrates a block sparsity constraint and support information which is estimated in an iterative fashion. The resulting optimization problem consists of a data fidelity term and a support detection based block sparsity (SDBS) promoting term penalizing entries within the complement of the estimated support. We provide optional strategies for block assignment, and we also derive unique and robust recovery conditions in terms of the structured restricted isometric property (RIP), namely the block-RIP. The block-RIP constant we derive is lower than that of the previous structured sparse method, which leads to a reduction of the measurements. Simulation results for reconstructing individual and multiple T1/T2-weighted images demonstrate the consistency with our theoretical claims, and show considerable improvement in comparison with methods using only block sparsity or support information.