Approximation theory of wavelet frame based image restoration (Q6652572)

Reconstructing images from degraded and incomplete measurements has always been a research hotspot in the field of image restoration. The paper proposes an image restoration model based on wavelet frames. This model minimizes the weighted norm of wavelet frame coefficients under certain constraints to achieve image restoration. By combining the law of large numbers and the covering number estimation, the error between the underlying original discrete image and the approximate solution in the discrete model is obtained, clearly demonstrating that under certain conditions, the restoration error can be effectively controlled. Furthermore, based on the multiresolution analysis of wavelet frames, the discrete image is related to the underlying continuous function, revealing the approximation relationship between the restored image and the underlying function, providing a new perspective for understanding the image restoration process from the function level. Some directions for expansion are also given.\N\NOverall, this paper has achieved remarkable results in the research of image restoration based on wavelet frames, laying a solid foundation for subsequent research. At the same time, the existing expandable directions also provide new research opportunities for researchers, which is expected to promote the continuous development of this field.