Application To MR Imaging With Iterative Support Detection Based On Compressed Sensing

Iterative support detection based on compressed sensing can be used in MRI, itnot only greatly reduces the sampling points but also increases reconstruction quality.Conventional MRI usually has a longer scan time which limits its clinicalapplications. Compressed sensing proposed by Candès and Donoho in2006breakstraditional Nyquist sampling theorem, and it uses nonlinear optimization algorithmto solve the problem of regularization, which greatly reduces the sampling amountneeded for reconstruction.The CS approach has three parts:(1) sparse representation, the desired image iscompressible or it has a sparse representation in a known transform domain.(2)sensing matrix, sensing matrix should be incoherent with the sparsifyng basis.(3)reconstruction algorithm, a nonlinear reconstruction should be used to enforce bothsparsity of the image representation and consistency.Existing reconstruction algorithm mainly contains three categories: greedypursuit algorithm, convex minimization method and the combination of these.However these algorithms only exploit sparsity information which is basicallyrequired as a priori in CS. Expansion of compressed sensing theory, such ascompressed Sensing with partial known support, not only exploits the spasityinformation, but also uses the known support information,which could furtherreduce the sampling points.Image reconstruction and support detection was alternately conducted in ISDwhich detects support after image reconstruction. In each iteration, the images werereconstructed through a truncated L1minimization. Specifically, the truncated L1minimization excludes the signal at the known support (detected from the previousiteration) from the cost function of the L1minimization. Once images werereconstructed in this iteration, the support information is updated by thresholding thereconstruction and used in next iteration (Those signals in the sparse representationof reconstructed images whose value was above the threshold were considered to besupport). As to the threshold, it gradually decreased with the increase of iteration number. With Iterative Supported Detection based-on compressed sensing, followingwork was done in this paper:(1) We applied ISD to T2map in MRI. ISD was combined with classicalnonlinear conjugate gradient reconstruction algorithm (NLCG) for imagereconstruction. After PCA (principal component analysis) was conducted on the lowresolution images, sparsifying basis was obtained. Support information was detectedin the reconstructed PC coefficient and used in the next iteration for reconstruction.After reconstruction of the T2-weighted images, T2maps were calculated using aconventional exponential least square fit. The experiment shows that T2map resultobtained by ISD compressed sensing method (PCA_ISD) is superior to the basiccompressed sensing method (PCA) from both the visual effect and T2evaluation.(2) How to apply ISD to the reconstruction of dynamic contrast-enhanced MRimages (DCE-MRI) was also studied.3D total variation was used as the sparsifyingbasis for DCE-MRI, support was detected in the3DTV sparse domain, then imageswere reconstructed by solving a truncated L1minimization. Experimental resultsshow that ISD method based on compressed sensing (3DTV_ISD) has a highersignal-to-noise ratio compared to the reconstructed image without ISD duringreconstruction (3DTV).