| Restoration is often performed on images to enhance salient features or remove degradation to assist in subsequent human or machine analysis. It is often necessary to restore several highly correlated images. These are produced when the same scene is imaged by more than one sensor and are called channels of that scene. Examples are the multiple frequency bands of satellite images, or the (red, green, and blue) channels of colored images.; The restoration problem for single-channel images has been well researched. However, treating separately each channel of a multi-channel image fails to utilize the cross channel correlations and thus results in suboptimal restorations. The extension of existing single channel restoration methods to multi-channel images is a non-trivial task. The main obstacle in this extension is the lack of computational algorithms for manipulating the matrices that appear in the multi-channel formulation of the restoration problem.; These matrices are block non-Toeplitz with large Toeplitz submatrices as elements. Using the Toeplitz to circulant approximation, the diagonalization properties of the Discrete Fourier transform, and the matrix inversion lemma, computational algorithms for the manipulation of these matrices were developed. These algorithms were than used to develope computational restoration filters that treat the entire multi-channel images as a single entity. These filters utilize both within and cross-channel correlations and thus are superior to treating each channel separately. Three multi-channel filters were formulated, implemented, and tested, the Wiener, the Kalman, and the least-squares filter. Experiments were performed where it was verified that incorporating cross-channel correlations improves the quality of the restored multi-channel images. |
