Data-Driven Tight Frame for Multi-channel Images and Its Application to Joint Color-Depth Image Reconstruction

In image restoration, we usually assume that the underlying image has a good sparse approximation under a certain system. Wavelet tight frame system has been proven to be such an efficient system to sparsely approximate piecewise smooth images. Thus, it has been widely used in many practical image restoration problems. However, images from different scenarios are so diverse that no static wavelet tight frame system can sparsely approximate all of them well. To overcome this, recently, Cai et. al. (Appl Comput Harmon Anal 37:89–105, 2014) proposed a method that derives a data-driven tight frame adapted to the specific input image, leading to a better sparse approximation. The data-driven tight frame has been applied successfully to image denoising and CT image reconstruction. In this paper, we extend this data-driven tight frame construction method to multi-channel images. We construct a discrete tight frame system for each channel and assume their sparse coefficients have a joint sparsity. The multi-channel data-driven tight frame construction scheme is applied to joint color and depth image reconstruction. Experimental results show that the proposed approach has a better performance than state-of-the-art joint color and depth image reconstruction approaches. © 2015, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press and Springer-Verlag Berlin Heidelberg.