Adaptive Dictionary Learning For Accelerating Magnetic Resonance Imaging

Compressed sensing utilizes the sparsity of the magnetic resonance image in the transform domain to accurately reconstruct the original signal from the highly undersampled k-space data. Compressed sensing theory demonstrates that the sparser the signal is, the better the reconstruction is. In traditional compressed sensing based magnetic resonance Imaging (MRI), the sparsifying transform is usually a global fixed transform, such as wavelet transform, discrete cosine transform (DCT) and finite difference transform. Recently, the patch based sparse representation with dictionary learning is becoming an important research trend. Dictionary learning is an adaptive sparse representation method, which can produce proper sparse representation according to the contents of different images. Compared with the global fixed transform, dictionary learning obtains more accurate sparse representation results because of its adaptivity. This property leads to the better image reconstruction in the framework of compressed sensing.This paper mainly discusses how to apply adaptive dictionary learning technique to magnetic resonance (MR) image reconstruction. The overlapping image patches are extracted from the images to learn a dictionary. The learned dictionary is used to sparsely represent the image patches. The dictionary and image patches are updated alternately to produce more accurate and effective sparse representation. This property ensures the quality of image reconstruction under highly undersampled rate.The contents of the thesis include:(1) A novel compressed sensing MRI method is proposed based on dictionary learning and wavelet subband decomposition. We discuss the relationship of wavelet domain and the k-space in order to decompose k-space data into local regions corresponding to different wavelet subbands. We estimate each localized region of k-space data by using the spectrum of each wavelet subband. In the reconstruction process, dictionary learning is applied on wavelet subbands, which produces sparser representation compared to the traditional strategy. Finally, inverse. wavelet transform is utilized to reconstruct the MR image. Experimental results indicate that the proposed method using dictionary learning achieves the more accurate image reconstruction performance than high frequency subband compressed sensing MRI.(2) A novel compressed sensing method for MR image sequence reconstruction is proposed based on structured sparse representation. Firstly, predefined patches are clustered, which are extracted from the degraded image sequence. Then the principal component analysis (PCA) is applied to each cluster and the PCA basis can be achieved. Each PCA basis is regarded as a sub-dictionary and all of the PCA bases constitute a whole structured sparse dictionary. Compared to the traditional overcomplete dictionary, the structured sparse dictionary reduces computational complexity and the degree of freedom in the estimations. Also, since the sub-dictionary corresponds to similar patches in the same cluster, it adds specificity to the patches and more accurate sparse representation can be obtained. Experimental results indicate that the proposed method with structured sparse representation obtains the more accurate image reconstruction performance than the state of the art method in dynamic MRI.