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

Evaluating Effect of Block Size in Compressed Sensing for Grayscale Images

Compressed sensing is an evolving methodology that enables sampling at sub-Nyquist rates and still provides decent signal reconstruction. During the last decade, the reported works have suggested to improve time efficiency by adopting Block based Compressed Sensing (BCS) and reconstruction performance improvement through new algorithms. A trade-off is required between the time efficiency and reconstruction quality. In this paper we have evaluated the significance of block size in BCS to improve reconstruction performance for grayscale images. A parameter variant of BCS [15] based sampling followed by reconstruction through Smoothed Projected Landweber (SPL) technique [16] involving use of Weiner smoothing filter and iterative hard thresholding is applied in this paper. The BCS variant is used to evaluate the effect of block size on image reconstruction quality by carrying out extensive testing on 9200 images acquired from online resources provided by Caltech101 [6], University of Granada [7] and Florida State University [8]. The experimentation showed some consistent results which can improve reconstruction performance in all BCS frameworks including BCS-SPL [17] and its variants [19], [27]. Firstly, the effect of varying block size (4x4, 8x8, 16x16, 32x32 and 64x64) results in changing the Peak Signal to Noise Ratio (PSNR) of reconstructed images from at least 1 dB to a maximum of 16 dB. This challenges the common notion that bigger block sizes always result in better reconstruction performance. Secondly, the variation in reconstruction quality with changing block size is mostly dependent on the image visual contents. Thirdly, images having similar visual contents, irrespective of the size, e.g., those from the same category of Caltech101 [6] gave majority vote for the same Optimum Block Size (OBS). These focused notes may help improve BCS based image capturing at many of the existing applications. For example, experimental results suggest using block size of 8x8 or 16x16 to capture facial identity using BCS. Fourthly, the average processing time taken for BCS and reconstruction through SPL with Lapped transform of Discrete Cosine Transform as the sparifying basis remained 300 milli-seconds for block size of 4x4 to 5 seconds for block size of 64x64. Since the processing time variation remains less than 5 seconds, selecting the OBS may not affect the time constraint in many applications. Analysis reveals that no particular block size is able to provide optimum reconstruction for all images with varying nature of visual contents. Therefore, the selection of block size should be made specific to the particular type of application images depending upon their visual contents