Convex optimization and greedy iterative algorithms for dictionary learning in the presence of Rician noise


  • M. V. R. Manimala
  • C. C.Dhanunjaya Naidu
  • M. N. Giri Prasad





Compressive Sensing, Convex Techniques, Greedy Iterative Algorithms, Magnetic Resonance Imaging.


Compressive Sensing (CS) is the emerging trend of recovering signal/image accurately from samples acquired at a rate far below the Nyquist rate. MR imaging provides a natural fit for applying CS as they can be sparsely represented in the transform domain. Magnitude MR images are corrupted by noise which follows Rician distribution and is difficult to remove as it is image dependent. Sparse coding is an important stage in dictionary learning. In this paper an attempt is being made to bring out a sparse coding technique which can provide better reconstruction in the presence of Rician noise. Greedy iterative algorithms and convex solutions are widely used for sparse coding. In the present work, performance of greedy algorithms, namely, Orthogonal Matching Pursuit (OMP) and Compressive Sampling Matching Pursuit (CoSaMP) have been evaluated and compared with convex techniques viz. Basis Pursuit (BP) and Least Absolute Shrinkage and Selection Operator (LASSO) in the sparse coding stage of an adaptive patch-based dictionary learning. Experiments have been carried out by varying Rician noise level from 0 to 30 and sparsity threshold per patch on MR images, acquired by employing various sampling schemes. Results show that greedy algorithms achieve higher PSNR and have very high computational speed compared to convex techniques when the MR images are corrupted with Rician noise.




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