Accelerating CS in Parallel Imaging Reconstructions Using an Efficient and Effective Circulant Preconditioner

摘要

Purpose: Design of a preconditioner for fast and efficient parallel imagingand compressed sensing reconstructions. Theory: Parallel imaging and compressedsensing reconstructions become time consuming when the problem size or thenumber of coils is large, due to the large linear system of equations that hasto be solved in l_1 and l_2-norm based reconstruction algorithms. Such linearsystems can be solved efficiently using effective preconditioning techniques.Methods: In this paper we construct such a preconditioner by approximating thesystem matrix of the linear system, which comprises the data fidelity andincludes total variation and wavelet regularization, by a matrix with theassumption that is a block circulant matrix with circulant blocks. Due to itscirculant structure, the preconditioner can be constructed quickly and itsinverse can be evaluated fast using only two fast Fourier transformations. Wetest the performance of the preconditioner for the conjugate gradient method asthe linear solver, integrated into the Split Bregman algorithm. Results: Thedesigned circulant preconditioner reduces the number of iterations required inthe conjugate gradient method by almost a factor of~5. The speed up results ina total acceleration factor of approximately 2.5 for the entire reconstructionalgorithm when implemented in MATLAB, while the initialization time of thepreconditioner is negligible. Conclusion: The proposed preconditioner reducesthe reconstruction time for parallel imaging and compressed sensing in a SplitBregman implementation and can easily handle large systems since it isFourier-based, allowing for efficient computations. Key words: preconditioning; compressed sensing; Split Bregman; parallelimaging