Abstract
A sparsifying transform for use in Compressed Sensing (CS) is a vital piece of image reconstruction for Magnetic Resonance Imaging (MRI). Previously, Translation Invariant Wavelet Transforms (TIWT) have been shown to perform exceedingly well in CS by reducing repetitive line pattern image artifacts that may be observed when using orthogonal wavelets. To further establish its validity as a good sparsifying transform, the TIWT is comprehensively investigated and compared with Total Variation (TV), using six under-sampling patterns through simulation. Both trajectory and random mask based under-sampling of MRI data are reconstructed to demonstrate a comprehensive coverage of tests. Notably, the TIWT in CS reconstruction performs well for all varieties of under-sampling patterns tested, even for cases where TV does not improve the mean squared error. This improved Image Quality (IQ) gives confidence in applying this transform to more CS applications which will contribute to an even greater speed-up of a CS MRI scan. High vs low resolution time of flight MRI CS re-constructions are also analyzed showing how partial Fourier acquisitions must be carefully addressed in CS to prevent loss of IQ. In the spirit of reproducible research, novel software is introduced here as FastTestCS. It is a helpful tool to quickly develop and perform tests with many CS customizations. Easy integration and testing for the TIWT and TV minimization are exemplified. Simulations of 3D MRI datasets are shown to be efficiently distributed as a scalable solution for large studies. Comparisons in reconstruction computation time are made between the Wavelab toolbox and Gnu Scientific Library in FastTestCS that show a significant time savings factor of 60×. The addition of FastTestCS is proven to be a fast, flexible, portable and reproducible simulation aid for CS research.
Highlights
Magnetic Resonance Imaging (MRI) is a diagnostic modality used to create in-vivo images of 3-Dimensional (3D) biological tissue utilizing magnetic fields, gradients and receivers
High vs low resolution time of flight MRI Compressed Sensing (CS) reconstructions are analyzed showing how partial Fourier acquisitions must be carefully addressed in CS to prevent loss of Image Quality (IQ)
When MR signal k-space data are fully sampled based on the Nyquist sampling criteria, some typical high resolution scans take five minutes, allowing time for patient and biologic movement, which negatively impacts Image Quality (IQ)
Summary
Magnetic Resonance Imaging (MRI) is a diagnostic modality used to create in-vivo images of 3-Dimensional (3D) biological tissue utilizing magnetic fields, gradients and receivers. When MR signal k-space data are fully sampled based on the Nyquist sampling criteria, some typical high resolution scans take five minutes, allowing time for patient and biologic movement, which negatively impacts Image Quality (IQ). A promising theory is Compressed Sensing (CS) to under-sample k-space below what the Nyquist criteria requires without compromising IQ. Candès et al and Lustig et al state a CS requirement of incoherence between the under-sampling domain and the sparse representation domain [1] [2]. This means that under-sampling in k-space must have artifacts that are incoherent in the linear image reconstruction. Sampling is costly in time, determining the shortest sample trajectory path is desired
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