Noiselet Encoded Compressive Sensing Parallel MRI

Kamlesh Pawar, Arjun Arunachalam, Gary F. Egan, and Jingxin Zhang


Magnetic Resonance Imaging, Noiselets, Compressed Sensing, Parallel Imaging


Compressed sensing (CS) reconstruction relies on the sparsity of the signal in the transform domain and on the incoherence between sensing and sparsifying transform matrices. In CS-MRI, the sensing matrix is the randomly undersampled Discrete Fourier transform (DFT) matrix while Wavelet is used as the sparsifying transform. However the incoherence between the DFT and the Wavelet transform matrices is suboptimal for CS-MRI. In this paper we investigated the use of Noiselets as sensing matrix in MRI in order to improve the incoherence between sensing and sparsifying transform matrices. Noiselet basis are totally incompressible by Wavelets and spread out energy of the Wavelets in the Noiselet domain. In this work the k-space is encoded with Noiselet basis in the primary phase encode direction and a few random phase encodes are taken for the CS reconstruction. We compared the CS reconstruction error with uniform undersampling of the Fourier encoded and the Noiselet encoded MR images for various reduction factors in simulation, and showed that Noiselet encoded MRI performs better than Fourier encoded MRI. However for pseudo random undersampling in the Fourier domain and uniform random undersampling in the Noiselet domain both techniques perform equally well. However when both Noiselet encoded and Fourier encoded CS-MRI techniques were combined with parallel imaging using distributed compressed sensing model, the Noiselet encoded CS-MRI with uniform random undersampling outperforms the Fourier encoded CS-MRI with pseudo random undersampling. A tailored spin echo sequence is proposed to encode primary phase encode direction with Noiselet basis for MR imaging.

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