Window-Based Convolutional Sparse Coding: Towards A Unified Framework

Sparse Coding (SC) and Convolution Sparse Coding (CSC) are two widely studied sparse methods in computer vision and signal processing. SC encodes the image patches independently, however fails to utilize the correlation among them. CSC adopts a convolution operator to connect the overlapping patches but in an inflexible manner. In this paper, a novel integrated framework for the two sparse models is proposed, wherein the local correlations among patches are controllable by manipulating a window function. Moreover, the inherent border effect of a convolution model is mitigated with a carefully designed weight function. It can be demonstrated that both SC and CSC are two distinct implementations of this framework. Consequently, our unified framework provides a balanced solution by addressing the strengths and limitations of both SC and CSC. Extensive experimental results are presented to demonstrate the superiority and effectiveness of the proposed method for image inpainting tasks.