Array imaging of localized objects in homogeneous and heterogeneous media

We present a comprehensive study of the resolution and stability properties of sparse promoting optimization theories applied to narrow band array imaging of localized scatterers. We consider homogeneous and heterogeneous media, and multiple and single scattering situations. When the media is homogeneous with strong multiple scattering between scatterers, we give a non-iterative formulation to find the locations and reflectivities of the scatterers from a nonlinear inverse problem in two steps, using either single or multiple illuminations. We further introduce an approach that uses the top singular vectors of the response matrix as optimal illuminations, which improves the robustness of sparse promoting optimization with respect to additive noise. When multiple scattering is negligible, the optimization problem becomes linear and can be reduced to a hybrid-$\ell_1$ method when optimal illuminations are used. When the media is random, and the interaction with the unknown inhomogeneities can be primarily modeled by wavefront distortions, we address the statistical stability of these methods. We analyze the fluctuations of the images obtained with the hybrid-$\ell_1$ method, and we show that it is stable with respect to different realizations of the random medium provided the imaging array is large enough. We compare the performance of the hybrid-$\ell_1$ method in random media to the widely used Kirchhoff migration and the multiple signal classification methods

PURIFY: a new algorithmic framework for next-generation radio-interferometric imaging

In recent works, compressed sensing (CS) and convex opti- mization techniques have been applied to radio-interferometric imaging showing the potential to outperform state-of-the-art imaging algorithms in the field. We review our latest contributions [1, 2, 3], which leverage the versatility of convex optimization to both handle realistic continuous visibilities and offer a highly parallelizable structure paving the way to significant acceleration of the reconstruction and high-dimensional data scalability. The new algorithmic structure promoted in a new software PURIFY (beta version) relies on the simultaneous-direction method of multipliers (SDMM). The performance of various sparsity priors is evaluated through simulations in the continuous visibility setting, confirming the superiority of our recent average sparsity approach SARA

Simultaneous use of Individual and Joint Regularization Terms in Compressive Sensing: Joint Reconstruction of Multi-Channel Multi-Contrast MRI Acquisitions

Purpose: A time-efficient strategy to acquire high-quality multi-contrast images is to reconstruct undersampled data with joint regularization terms that leverage common information across contrasts. However, these terms can cause leakage of uncommon features among contrasts, compromising diagnostic utility. The goal of this study is to develop a compressive sensing method for multi-channel multi-contrast magnetic resonance imaging (MRI) that optimally utilizes shared information while preventing feature leakage. Theory: Joint regularization terms group sparsity and colour total variation are used to exploit common features across images while individual sparsity and total variation are also used to prevent leakage of distinct features across contrasts. The multi-channel multi-contrast reconstruction problem is solved via a fast algorithm based on Alternating Direction Method of Multipliers. Methods: The proposed method is compared against using only individual and only joint regularization terms in reconstruction. Comparisons were performed on single-channel simulated and multi-channel in-vivo datasets in terms of reconstruction quality and neuroradiologist reader scores. Results: The proposed method demonstrates rapid convergence and improved image quality for both simulated and in-vivo datasets. Furthermore, while reconstructions that solely use joint regularization terms are prone to leakage-of-features, the proposed method reliably avoids leakage via simultaneous use of joint and individual terms. Conclusion: The proposed compressive sensing method performs fast reconstruction of multi-channel multi-contrast MRI data with improved image quality. It offers reliability against feature leakage in joint reconstructions, thereby holding great promise for clinical use.Comment: 13 pages, 13 figures. Submitted for possible publicatio