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.
In the present study, a new Lieb lattice with five points(hereinafter referred to as Lieb-5 lattice) in the minimum periodic unit is used as a platform. The sites of Lieb-5 lattices are classified into two categories according to their spatial position, respectively, the center lattice and the edge lattices. We investigate the effect of two categories lattices with different intensity on the propagation of the out-of-phase octupole beam. According to simulation results, when the intensity of the center lattice is less than that of the edge lattices(the ratio of two lattice intensities is 2:3), eight-peak shape is always maintained during beam propagation, presenting “strong localization”. Otherwise, the energy between incident lattices is periodically coupled with the increase of propagation distance, presenting “weak localization.”
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.