A fast procedure for acquisition and reconstruction of magnetic resonance images using compressive sampling

This paper proposes a fast and robust procedure for sensing and reconstruction of sparse or compressible magnetic resonance images based on the compressive sampling theory. The algorithm starts with incoherent undersampling of the k-space data of the image using a random matrix. The undersampled data is sparsified using Haar transformation. The Haar transform coefficients of the k-space data are then reconstructed using the orthogonal matching Pursuit algorithm. The reconstructed coefficients are inverse transformed into k-space data and then into the image in spatial domain. Finally, a median filter is used to suppress the recovery noise artifacts. Experimental results show that the proposed procedure greatly reduces the image data acquisition time without significantly reducing the image quality. The results also show that the error in the reconstructed image is reduced by median filtering.