We consider the problem of recovering complex-valued block sparse signals with unknown borders. Such signals arise naturally in numerous applications. Several algorithms have been developed to solve the problem of unknown block partitions. In pattern-coupled sparse Bayesian learning (PCSBL), each coefficient involves its own hyperparameter and those of its immediate neighbors to exploit the block sparsity. Extended block sparse Bayesian learning (EBSBL) assumes the block sparse signal consists of correlated and overlapping blocks to enforce block correlations. We propose a simpler alternative to EBSBL and reveal the underlying relationship between the proposed method and a particular case of EBSBL. The proposed algorithm uses the fact that immediate neighboring sparse coefficients are correlated. The proposed model is similar to classical sparse Bayesian learning (SBL). However, unlike the diagonal correlation matrix in conventional SBL, the unknown correlation matrix has a tridiagonal structure to capture the correlation with neighbors. Due to the entanglement of the elements in the inverse tridiagonal matrix, instead of a direct closed-form solution, an approximate solution is proposed. The alternative algorithm avoids the high dictionary coherence in EBSBL, reduces the unknowns of EBSBL, and is computationally more efficient. The sparse reconstruction performance of the algorithm is evaluated with both correlated and uncorrelated block sparse coefficients. Simulation results demonstrate that the proposed algorithm outperforms PCSBL and correlation-based methods such as EBSBL in terms of reconstruction quality. The numerical results also show that the proposed correlated SBL algorithm can deal with isolated zeros and nonzeros as well as block sparse patterns.

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It has been previously demonstrated that applying an aberrating mask for 2D compressive imaging using a low number of sensors (elements) can significantly improve image resolution, as evaluated via the point spread function. Here we investigate the potential to apply a similar approach for 3D flow monitoring. We conducted a 3D k-Wave simulation using a 5x5 sensor array coupled to a physical coding mask, performing B-mode and power Doppler imaging on a 3D carotid artery flow model. An approximately three times smaller lateral PSF was achieved at the cost of increased background clutter level and slightly increased axial PSF. A better definition of the vessel border and finer flow speckle were observed in power Doppler imaging. Our results suggest that 3D compressive imaging using a very low sensor count of 25 with spatial coding mask has the potential to monitor 3D carotid artery flow.@en

We consider the problem of recovering block-sparse signals with unknown boundaries. Such signals arise naturally in various applications. Recent literature introduced a pattern-coupled or clustered Gaussian prior, in which each coefficient involves its own hyperparameter as well as its immediate neighbors' hyperparameters. Some methods use a hierarchical distribution making the solution vulnerable to the parameter choice. Besides, these methods mainly rely on the expectation-maximization (EM) algorithm and either require a suboptimal solution or an approximation of the hyperparameters. To address these difficulties, we propose to solve the pattern coupling problem via fixed point iterations instead of the EM algorithm. The proposed algorithm does not require any further assumptions on the hyperparameters and provides a simple update rule for the hyperparameters. Although the fixed point iterations method is an empirical strategy, it provides a fast convergence rate. The proposed algorithm is tested on a simple direction of arrival (DOA) and amplitude estimation problem. From our simulations, we see that the proposed method achieves similar reconstruction results with the state-of-the-art; however, the proposed method is faster than the existing counterparts.@en

We intend to develop an ultrasound compressive imaging device to perform carotid artery (CA) function and flow monitoring/imaging by using just a few single element transducers equipped with spatial coding masks. The spatially unique impulse responses can be exploited in compressive reconstructions. To explore the potential of different configurations, in this study we emulated such a device using a linear array system. We combined its elements with individual digital delays into a small number of groups. The results suggest our spatial coding mask approach based on reconstructions regularized with a least squares method has potential for CA monitoring with only 10 to 12 sensors.

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Ultrasound imaging of the vasculature has major significance for the detection of cardiovascular diseases and cancer. However, limited spatial resolution or long acquisition times of existing techniques limit the visualization of the microvascular structures. Enforcing sparsity in the underlying vasculature as well as exploiting statistical independence between voxels have become prominent for fast super-resolution imaging. However, such a statistical independence may not be valid for all voxels and may hence lead to a distorted signal model. Here we present an image reconstruction method that exploits the sparsity of the vasculature data without distorting the original signal model. We employ a multiple measurement vector (MMV) model to enforce the joint sparsity over the images at different time instants. To reduce the computational complexity of obtaining the solution, the ℓ1-SVD method is applied to the MMV model. We demonstrate that our method improves spatial resolution and provides a clear separation between blood vessels. Although our method is slightly slower than existing approaches, it outperforms them in terms of image reconstruction quality.@en