LAUSR

Abstract. We propose the fractional-order total variation (TV) algorithm with nonlocal self-similarity for image reconstruction in compressed sensing to alleviate texture details deterioration and eliminate staircase artifacts, which results from the TV algorithms. The Grünwald–Letnikov fractional-order differential operators, which consider more neighboring image pixels and use four different directions to handle fractional-order gradients, are used to replace the integer-order differential operators. To suppress the staircase artifacts, modified nonlocal means operators are introduced into our method, which can contain prior image structural information and update the Lagrangian multipliers. An efficient augmented Lagrangian algorithm is used to solve the TV problem. Numerical results show that the algorithm achieves remarkable performance improvements at various sampling ratios. Compared with fractional-order TV-based projections onto convex sets, the maximum gains of peak signal-to-noise ratio and structural similarity index with all images are up to 2.52 dB and 0.0178, respectively, and the algorithm performs the better for preserving details and eliminating the staircase effect at the cost of taking more time.