Half-quadratic regularization for MRI image restoration

We consider the reconstruction of MRI images by minimizing regularized cost-functions. To accelerate the computation of the estimate, two forms of half-quadratic regularization, multiplicative and additive, are often used. In Nikolova and Ng (2002), we have compared both theoretically and experimentally the efficiency of these two forms using one-dimensional signals. The goal of this paper is to compare experimentally the efficiency of these two forms using MRI image reconstruction. We find that using the additive form is more computationally effective than using the multiplicative form.published_or_final_versio

ISTA-Net: Interpretable Optimization-Inspired Deep Network for Image Compressive Sensing

With the aim of developing a fast yet accurate algorithm for compressive sensing (CS) reconstruction of natural images, we combine in this paper the merits of two existing categories of CS methods: the structure insights of traditional optimization-based methods and the speed of recent network-based ones. Specifically, we propose a novel structured deep network, dubbed ISTA-Net, which is inspired by the Iterative Shrinkage-Thresholding Algorithm (ISTA) for optimizing a general $\ell_1$ norm CS reconstruction model. To cast ISTA into deep network form, we develop an effective strategy to solve the proximal mapping associated with the sparsity-inducing regularizer using nonlinear transforms. All the parameters in ISTA-Net (\eg nonlinear transforms, shrinkage thresholds, step sizes, etc.) are learned end-to-end, rather than being hand-crafted. Moreover, considering that the residuals of natural images are more compressible, an enhanced version of ISTA-Net in the residual domain, dubbed {ISTA-Net}$^+$, is derived to further improve CS reconstruction. Extensive CS experiments demonstrate that the proposed ISTA-Nets outperform existing state-of-the-art optimization-based and network-based CS methods by large margins, while maintaining fast computational speed. Our source codes are available: \textsl{http://jianzhang.tech/projects/ISTA-Net}.Comment: 10 pages, 6 figures, 4 Tables. To appear in CVPR 201

Image Restoration Using Functional and Anatomical Information Fusion with Application to SPECT-MRI Images

Image restoration is usually viewed as an ill-posed problem in image processing, since there is no unique solution associated with it. The quality of restored image closely depends on the constraints imposed of the characteristics of the solution. In this paper, we propose an original extension of the NAS-RIF restoration technique by using information fusion as prior information with application in SPECT medical imaging. That extension allows the restoration process to be constrained by efficiently incorporating, within the NAS-RIF method, a regularization term which stabilizes the inverse solution. Our restoration method is constrained by anatomical information extracted from a high resolution anatomical procedure such as magnetic resonance imaging (MRI). This structural anatomy-based regularization term uses the result of an unsupervised Markovian segmentation obtained after a preliminary registration step between the MRI and SPECT data volumes from each patient. This method was successfully tested on 30 pairs of brain MRI and SPECT acquisitions from different subjects and on Hoffman and Jaszczak SPECT phantoms. The experiments demonstrated that the method performs better, in terms of signal-to-noise ratio, than a classical supervised restoration approach using a Metz filter