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

Robust Deep Compressive Sensing with Recurrent-Residual Structural Constraints

Existing deep compressive sensing (CS) methods either ignore adaptive online optimization or depend on costly iterative optimizer during reconstruction. This work explores a novel image CS framework with recurrent-residual structural constraint, termed as R$^2$CS-NET. The R$^2$CS-NET first progressively optimizes the acquired samplings through a novel recurrent neural network. The cascaded residual convolutional network then fully reconstructs the image from optimized latent representation. As the first deep CS framework efficiently bridging adaptive online optimization, the R$^2$CS-NET integrates the robustness of online optimization with the efficiency and nonlinear capacity of deep learning methods. Signal correlation has been addressed through the network architecture. The adaptive sensing nature further makes it an ideal candidate for color image CS via leveraging channel correlation. Numerical experiments verify the proposed recurrent latent optimization design not only fulfills the adaptation motivation, but also outperforms classic long short-term memory (LSTM) architecture in the same scenario. The overall framework demonstrates hardware implementation feasibility, with leading robustness and generalization capability among existing deep CS benchmarks

Plug-and-Play Algorithms for Video Snapshot Compressive Imaging

We consider the reconstruction problem of video snapshot compressive imaging (SCI), which captures high-speed videos using a low-speed 2D sensor (detector). The underlying principle of SCI is to modulate sequential high-speed frames with different masks and then these encoded frames are integrated into a snapshot on the sensor and thus the sensor can be of low-speed. On one hand, video SCI enjoys the advantages of low-bandwidth, low-power and low-cost. On the other hand, applying SCI to large-scale problems (HD or UHD videos) in our daily life is still challenging and one of the bottlenecks lies in the reconstruction algorithm. Exiting algorithms are either too slow (iterative optimization algorithms) or not flexible to the encoding process (deep learning based end-to-end networks). In this paper, we develop fast and flexible algorithms for SCI based on the plug-and-play (PnP) framework. In addition to the PnP-ADMM method, we further propose the PnP-GAP (generalized alternating projection) algorithm with a lower computational workload. We first employ the image deep denoising priors to show that PnP can recover a UHD color video with 30 frames from a snapshot measurement. Since videos have strong temporal correlation, by employing the video deep denoising priors, we achieve a significant improvement in the results. Furthermore, we extend the proposed PnP algorithms to the color SCI system using mosaic sensors, where each pixel only captures the red, green or blue channels. A joint reconstruction and demosaicing paradigm is developed for flexible and high quality reconstruction of color video SCI systems. Extensive results on both simulation and real datasets verify the superiority of our proposed algorithm.Comment: 18 pages, 12 figures and 4 tables. Journal extension of arXiv:2003.13654. Code available at https://github.com/liuyang12/PnP-SCI_pytho

Compressive sensing based Bayesian sparse channel estimation for OFDM communication systems: high performance and low complexity

In orthogonal frequency division modulation (OFDM) communication systems, channel state information (CSI) is required at receiver due to the fact that frequency-selective fading channel leads to disgusting inter-symbol interference (ISI) over data transmission. Broadband channel model is often described by very few dominant channel taps and they can be probed by compressive sensing based sparse channel estimation (SCE) methods, e.g., orthogonal matching pursuit algorithm, which can take the advantage of sparse structure effectively in the channel as for prior information. However, these developed methods are vulnerable to both noise interference and column coherence of training signal matrix. In other words, the primary objective of these conventional methods is to catch the dominant channel taps without a report of posterior channel uncertainty. To improve the estimation performance, we proposed a compressive sensing based Bayesian sparse channel estimation (BSCE) method which can not only exploit the channel sparsity but also mitigate the unexpected channel uncertainty without scarifying any computational complexity. The propose method can reveal potential ambiguity among multiple channel estimators that are ambiguous due to observation noise or correlation interference among columns in the training matrix. Computer simulations show that propose method can improve the estimation performance when comparing with conventional SCE methods.Comment: 24 pages,16 figures, submitted for a journa