  This study proposes a convolutional nonlinear dictionary (CNLD) for image
restoration using cascaded filter banks. Generally, convolutional neural
networks (CNN) demonstrate their practicality in image restoration
applications; however, existing CNNs are constructed without considering the
relationship among atomic images (convolution kernels). As a result, there
remains room for discussing the role of design spaces. To provide a framework
for constructing an effective and structured convolutional network, this study
proposes the CNLD. The backpropagation learning procedure is derived from
certain image restoration experiments, and thereby the significance of CNLD is
verified. It is demonstrated that the number of parameters is reduced while
preserving the restoration performance.
