Kamlesh Pawar, Arjun Arunachalam, Gary F. Egan
Magnetic Resonance Imaging, Noiselets, CompressedSensing, Parallel Imaging, Non Fourier Encoding
Compressed sensing (CS) reconstruction relies on the spar- sity of the signal in the transform domain and on the in- coherence between sensing and sparsifying transform ma- trices. In CS-MRI, the sensing matrix is the randomly un- dersampled 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 in- vestigated 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 reconstruc- tion error with uniform undersampling of the Fourier en- coded 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 Noise- let domain both techniques perform equally well. However when both Noiselet encoded and Fourier encoded CS-MRI techniques were combined with parallel imaging using dis- tributed compressed sensing model, the Noiselet encoded CS-MRI with uniform random undersampling outperforms the Fourier encoded CS-MRI with pseudo random under- sampling. A tailored spin echo sequence is proposed to encode primary phase encode direction with Noiselet basis for MR imaging.
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