Fast image inpainting using exponential-threshold POCS plus conjugate gradient

Abstract

Image inpainting can remove unwanted objects and reconstruct the missing or damaged portions of an image. The projection onto convex sets (POCS) is a classical method used in image inpainting. However, the traditional POCS converges slowly due to the linear error threshold. We propose an exponential-threshold scheme, which greatly improves the convergence of the POCS. Although the exponential-threshold POCS can recover the image in about 20 iterations, it cannot reconstruct the image details very well even with hundreds of iterations. Thus, we append the non-local restoration to the exponential-threshold POCS to further refine the image details, and then we solve this objective function using the conjugate gradient. Numerical experiments show that for each iteration, the exponential-threshold POCS and the conjugate gradient have very similar computational efficiencies. For an image with various topologies of the missing areas, our scheme can recover missing pixels simultaneously and obtain a satisfied inpainting result in only 20 iterations of the exponential-threshold POCS and 20 iterations of the conjugate gradient. The proposed method can excellently restore damaged photographs and remove superimposed text. This method has less computational cost than the conjugate gradient and has a higher resolution than the POCS.

Image Super-Resolution Reconstruction Based on Sparse Representation and POCS Method

“…POCS method can reconstruct a super-resolution image form LR images, and not only restore the details, but also amplify the dimension of a LR image [7,8]. It is an iteration and projection process, which starts from a given or random initial image in the Hilbert space.…”

“…(9) is a NP problem, to obtain unique solution, some algorithms, such as basis pursuit (BP), OMP, regularized OMP (ROMP) [16], Stage-wise OMP (StOMP) [7] and so on. Onceŝ estimated is enough to be sparse, and thenŝ is thought to approach the exact solution, thus, the estimation of x can be obtained by the formula ofx ¼ Dŝ.…”

“…Spatial methods use general observation models, which have better adaptability and performance and they are used generally now [3]. To this day, some spatial methods used widely contain iterative back projection (IBP) [4,5], non-uniformly interval sample interpolation [5], constrained least square (CLS) [6], self-adaptive filter [3], project onto convex set (POCS) [2,3,7,8], maximum a posteriori probability estimation (MAP) and so on [8]. Among these methods, POCS method can keep well edge features of an image and be flexibly added prior information, so it is utilized widely in image processing fields.…”

A fast-convergence POCS seismic denoising and reconstruction method

“…Wang and Zhang (2014) analyzed the effect of the interval between two neighboring threshold on convergence and developed a new exponential threshold to further speed the convergence of POCS reconstruction algorithm.…”

Deblocking Artifact of Satellite Image Based on Adaptive Soft-Threshold Anisotropic Filter Using Wavelet

“…POCS uses a dynamic focus-plus context (DF+C) [13] and the improved weighted projection onto convex sets (IWPOCS) [14]. The techniques make good effects, but the main disadvantages of DF+C and IWPOCS methods are non-unique solution, always slow convergence, high computational time [15] and also unstable of numerical computation [16] in reconstruction of the detailed structures of the satellite image. The other disadvantages of spatially adaptive techniques in DF+C and IWPOCS methods are much greater precomputation and searching processes than wavelet transform, and also the limited reference of the satellite image.…”