Investigation of Sparsifying Transforms in Compressed Sensing for Magnetic Resonance Imaging with Fasttestcs

The goal of this contribution is to achieve higher reduction factors for faster Magnetic Resonance Imaging (MRI) scans with better Image Quality (IQ) by using Compressed Sensing (CS). This can be accomplished by adopting and understanding better sparsifying transforms for CS in MRI. There is a tremendous number of transforms and optional settings potentially available. Additionally, the amount of research in CS is growing, with possible duplication and difficult practical evaluation and comparison. However, no in-depth analysis of the effectiveness of different redundant sparsifying transforms on MRI images with CS has been undertaken until this work. New theoretical sparsity bounds for the dictionary restricted isometry property constants in CS are presented with mathematical proof. In order to verify the sparsifying transforms in this setting, the experiments focus on several redundant transforms contrasting them with orthogonal transforms. The transforms investigated are Wavelet (WT), Cosine (CT), contourlet, curvelet, k-means singular value decomposition, and Gabor. Several variations of these transforms with corresponding filter options are developed and tested in compression and CS simulations. Translation Invariance (TI) in transforms is found to be a key contributing factor in producing good IQ because any particular translation of the signal will not effect the transform representation. Some transforms tested here are TI and many others are made TI by transforming small overlapping image patches. These transforms are tested by comparing different under-sampling patterns and reduction ratios with varying image types including MRI data. Radial, spiral, and various random patterns are implemented and demonstrate that the TIWT is very robust across all under-sampling patterns. Results of the TIWT simulations show improvements in de-noising and artifact suppression over that of individual orthogonal wavelets and total variation ell-1 minimization in CS simulations. Some of these transforms add considerable time to the CS simulations and prohibit extensive testing of large 3D MRI datasets. Therefore, the FastTestCS software simulation framework is developed and customized for testing images, under-samping patterns and sparsifying transforms. This novel software is offered as a practical, robust, universal framework for evaluating and developing simulations in order to quickly test sparsifying transforms for CS MRI

Edge Guided Reconstruction for Compressive Imaging

We propose EdgeCS—an edge guided compressive sensing reconstruction approach—to recover images of higher quality from fewer measurements than the current methods. Edges are important image features that are used in various ways in image recovery, analysis, and understanding. In compressive sensing, the sparsity of image edges has been successfully utilized to recover images. However, edge detectors have not been used on compressive sensing measurements to improve the edge recovery and subsequently the image recovery. This motivates us to propose EdgeCS, which alternatively performs edge detection and image reconstruction in a mutually beneficial way. The edge detector of EdgeCS is designed to faithfully return partial edges from intermediate image reconstructions even though these reconstructions may still have noise and artifacts. For complex-valued images, it incorporates joint sparsity between the real and imaginary components. EdgeCS has been implemented with both isotropic and anisotropic discretizations of total variation and tested on incomplete k-space (spectral Fourier) samples. It applies to other types of measurements as well. Experimental results on large-scale real/complex-valued phantom and magnetic resonance (MR) images show that EdgeCS is fast and returns high-quality images. For example, it exactly recovers the 256×256 Shepp–Logan phantom from merely 7 radial lines (3.03% k-space), which is impossible for most existing algorithms. It is able to accurately reconstruct a 512 × 512 MR image with 0.05 white noise from 20.87% radial samples. On complex-valued MR images, it obtains recoveries with faithful phases, which are important in many medical applications. Each of these tests took around 30 seconds on a standard PC. Finally, the algorithm is GPU friendly

Structured Sparsity: Discrete and Convex approaches

Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics applications: While the ambient dimension is vast in modern data analysis problems, the relevant information therein typically resides in a much lower dimensional space. However, many solutions proposed nowadays do not leverage the true underlying structure. Recent results in CS extend the simple sparsity idea to more sophisticated {\em structured} sparsity models, which describe the interdependency between the nonzero components of a signal, allowing to increase the interpretability of the results and lead to better recovery performance. In order to better understand the impact of structured sparsity, in this chapter we analyze the connections between the discrete models and their convex relaxations, highlighting their relative advantages. We start with the general group sparse model and then elaborate on two important special cases: the dispersive and the hierarchical models. For each, we present the models in their discrete nature, discuss how to solve the ensuing discrete problems and then describe convex relaxations. We also consider more general structures as defined by set functions and present their convex proxies. Further, we discuss efficient optimization solutions for structured sparsity problems and illustrate structured sparsity in action via three applications.Comment: 30 pages, 18 figure

Blip-Up Blip-Down Circular EPI (BUDA-cEPI) for Distortion-Free dMRI with Rapid Unrolled Deep Learning Reconstruction

Purpose: We implemented the blip-up, blip-down circular echo planar imaging (BUDA-cEPI) sequence with readout and phase partial Fourier to reduced off-resonance effect and T2* blurring. BUDA-cEPI reconstruction with S-based low-rank modeling of local k-space neighborhoods (S-LORAKS) is shown to be effective at reconstructing the highly under-sampled BUDA-cEPI data, but it is computationally intensive. Thus, we developed an ML-based reconstruction technique termed "BUDA-cEPI RUN-UP" to enable fast reconstruction. Methods: BUDA-cEPI RUN-UP - a model-based framework that incorporates off-resonance and eddy current effects was unrolled through an artificial neural network with only six gradient updates. The unrolled network alternates between data consistency (i.e., forward BUDA-cEPI and its adjoint) and regularization steps where U-Net plays a role as the regularizer. To handle the partial Fourier effect, the virtual coil concept was also incorporated into the reconstruction to effectively take advantage of the smooth phase prior, and trained to predict the ground-truth images obtained by BUDA-cEPI with S-LORAKS. Results: BUDA-cEPI with S-LORAKS reconstruction enabled the management of off-resonance, partial Fourier, and residual aliasing artifacts. However, the reconstruction time is approximately 225 seconds per slice, which may not be practical in a clinical setting. In contrast, the proposed BUDA-cEPI RUN-UP yielded similar results to BUDA-cEPI with S-LORAKS, with less than a 5% normalized root mean square error detected, while the reconstruction time is approximately 3 seconds. Conclusion: BUDA-cEPI RUN-UP was shown to reduce the reconstruction time by ~88x when compared to the state-of-the-art technique, while preserving imaging details as demonstrated through DTI application.Comment: Number: Figures: 8 Tables: 3 References: 7

Investigation of compressed-sensing for acceleration of magnetic resonance spectroscopic imaging

Magnetic Resonance Spectroscopic Imaging (MRSI) is a functional MRI technique allowing non-invasive biochemical mapping of the brain. MRSI is advantageous for characterising many neurological conditions; however, its clinical application is limited by lengthy scan time and low spatial resolution, which are intrinsically linked. This research investigated the potential of Compressed Sensing (CS) to speed-up MRSI or enhance spatial resolution. CS allows accelerated acquisition by reducing the data sampling requirements, whilst preserving image quality. The focus of this work was the effect of CS-MRSI at different acceleration factors upon spatial integrity. CS reconstruction software was developed and applied to retrospective MRSI data. Imaging test objects and software simulations were developed to assess MRSI spatial resolution via metabolite edge response measurements. CS-MRSI was also investigated in realistic scenarios using data from healthy volunteers and a child with Optic Pathway Glioma (OPG). The potential of CS-MRSI to enable high-resolution MRSI in feasible scan times was investigated using simulations of focal and infiltrative OPG. Results suggest that CS-MRSI can reduce scan duration by up to a factor of 5 whilst simultaneously eliminating ringing artefacts and increasing spatial resolution compared with conventionally filtered MRSI. Therefore, CS could greatly increase the clinical utility of MRSI