1 research outputs found
Image Inpainting Using Directional Tensor Product Complex Tight Framelets
In this paper we are particularly interested in the image inpainting problem
using directional complex tight wavelet frames. Under the assumption that frame
coefficients of images are sparse, several iterative thresholding algorithms
for the image inpainting problem have been proposed in the literature. The
outputs of such iterative algorithms are closely linked to solutions of several
convex minimization models using the balanced approach which simultaneously
combines the -regularization for sparsity of frame coefficients and the
-regularization for smoothness of the solution. Due to the redundancy of a
tight frame, elements of a tight frame could be highly correlated and
therefore, their corresponding frame coefficients of an image are expected to
close to each other. This is called the grouping effect in statistics. In this
paper, we establish the grouping effect property for frame-based convex
minimization models using the balanced approach. This result on grouping effect
partially explains the effectiveness of models using the balanced approach for
several image restoration problems. Inspired by recent development on
directional tensor product complex tight framelets (TP-CTFs) and their
impressive performance for the image denoising problem, in this paper we
propose an iterative thresholding algorithm using a single tight frame derived
from TP-CTFs for the image inpainting problem. Experimental results show that
our proposed algorithm can handle well both cartoons and textures
simultaneously and performs comparably and often better than several well-known
frame-based iterative thresholding algorithms for the image inpainting problem
without noise. For the image inpainting problem with additive zero-mean i.i.d.
Gaussian noise, our proposed algorithm using TP-CTFs performs superior than
other known state-of-the-art frame-based image inpainting algorithms