Abstract
The use of non-local self-similarity prior between image blocks can improve image reconstruction performance significantly. We propose a compressive sensing image reconstruction algorithm that combines bilateral total variation and nonlocal low-rank regularization to overcome over-smoothing and degradation of edge information which result from the prior reconstructed image. The proposed algorithm makes use of the preservation of image edge information by bilateral total variation operator to enhance the edge details of the reconstructed image. In addition, we use weighted nuclear norm regularization as a low-rank constraint for similar blocks of the image. To solve this convex optimization problem, the Alternating Direction Method of Multipliers (ADMM) is employed to optimize and iterate the algorithm model effectively. Experimental results show that the proposed algorithm can obtain better image reconstruction quality than conventional algorithms with using total variation regularization or considering the nonlocal structure of the image only. At 10% sampling rate, the peak signal-to-noise ratio gain is up to 2.39 dB in noiseless measurements compared with Nonlocal Low-rank Regularization (NLR-CS). Reconstructed image comparison shows that the proposed algorithm retains more high frequency components. In noisy measurements, the proposed algorithm is robust to noise and the reconstructed image retains more detail information.
Highlights
Compressive sensing (CS) [1,2,3] is a burgeoning signal acquisition and reconstruction method that breaks through the frequency limit of the Nyquist–Shannon sampling theorem
The greedy algorithms based on the l0 norm minimization model include Orthogonal Match Pursuit (OMP) [12], Subspace Pursuit (SP) [13], Compressed Sampling Match Pursuit (CoSaMP) [14], etc; The convex optimization algorithms based on the l1 norm minimization model include Basis Pursuit (BP) [15], Iterative Shrinkage Threshold (IST) [16], Gradient Projection (GP) [17], Total Variation (TV) [18], etc
+ε ; Calculate Lik+1 according to Equation (17); End for Calculate uk+1 according to Equation (20); Calculate zk+1 according to Equation (22), update the gradient weight wkb+1 according to Equation (23); Calculate xk+1 according to Equation (25); Update Lagrange multipliers ak+1, bk+1 according to Equation (15); if mod(k, T) = 0, relocate the similar blocks position and update similar blocks grouping; End for Output: The final reconstructed image x = xK
Summary
Compressive sensing (CS) [1,2,3] is a burgeoning signal acquisition and reconstruction method that breaks through the frequency limit of the Nyquist–Shannon sampling theorem. The total variation algorithm uses the sparse gradient prior as a constraint to reconstruct the image, which can remove the noise and retain the detail information of the image better. Some problems such as staircase effect still exist in the total variation algorithm. Zhang et al [25] introduced nonlocal mean filter as a regularization term into the total variation model and used the correlation of noise between image blocks to set weights for filtering, which achieves excellent constraint and reconstruction results. We add the bilateral total variation constraint as a global information prior to the reconstruction model based on nonlocal low-rank to propose an optimized scheme.
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