NOISELET ENCODED COMPRESSIVE SENSING PARALLEL MRI

摘要

Compressed sensing (CS) reconstruction relies on the sparsityof the signal in the transform domain and on the incoherencebetween sensing and sparsifying transform matrices.In CS-MRI, the sensing matrix is the randomly undersampledDiscrete Fourier transform (DFT) matrix whileWavelet is used as the sparsifying transform. However theincoherence between the DFT and the Wavelet transformmatrices is suboptimal for CS-MRI. In this paper we investigatedthe use of Noiselets as sensing matrix in MRIin order to improve the incoherence between sensing andsparsifying transform matrices. Noiselet basis are totallyincompressible by Wavelets and spread out energy of theWavelets in the Noiselet domain. In this work the k-spaceis encoded with Noiselet basis in the primary phase encodedirection and a few random phase encodes are taken forthe CS reconstruction. We compared the CS reconstructionerror with uniform undersampling of the Fourier encodedand the Noiselet encoded MR images for variousreduction factors in simulation, and showed that Noiseletencoded MRI performs better than Fourier encoded MRI.However for pseudo random undersampling in the Fourierdomain and uniform random undersampling in the Noiseletdomain both techniques perform equally well. Howeverwhen both Noiselet encoded and Fourier encoded CS-MRItechniques were combined with parallel imaging using distributedcompressed sensing model, the Noiselet encodedCS-MRI with uniform random undersampling outperformsthe Fourier encoded CS-MRI with pseudo random undersampling.A tailored spin echo sequence is proposed toencode primary phase encode direction with Noiselet basisfor MR imaging.