||This talk outlines a restoration process of high-dimensional signals such as image and volumetric data. With the development of measurement technology, it is now possible to acquire a large amount of physical data, and the demand for high performance signal restoration is increasing. In order to achieve high performance signal restoration, a generative model that can effectively represent the physical data of interest is required. The convolutional network model is one of the most powerful existing generative models. The model exploits the local relationships of signals and provides significant performance improvements in image recognition and restoration. However, it is difficult to reflect domain knowledge in the network structure, and theoretically supported systematic and strategic structure setting remains a challenge. Emergent issues occur particularly for data in unknown fields. Therefore, in this project, it is proposed to introduce the results of filter banks and optimization theory into a convolutional network. The purpose is to enable physically interpretable structural settings and to make the design and implementation efficient. We are attempting to create a convolutional network reflecting domain knowledge for various real data such as biological tomographic images, vehicle-mounted millimeter-wave radar images, and river observation data. In this talk, the construction of generative models using filter banks, their parametric learning designs and nonlinear extensions are reviewed. In addition, a comparison with existing methods based on convolutional neural networks (CNNs) is explained.