Inversion algorithm for the discrete periodic Radon transform and application on image restoration

The discrete periodic Radon transform (DPRT), which was proposed recently, has been shown to have many useful properties that enable a 2-D signal to be processed by some 1-D approaches. In this paper, the application of the DPRT in image restoration is studied. It is based on the fact that the phase information of an image is preserved when it is transformed by the DPRT. As the phase information is also not distorted by some types of blurring, we can make use of the transformed phase information of the blurred image to perform the restoration. The advantage of using the DPRT is that we can reduce the original 2-D restoration problem to become some 1-D ones, then, we make use of the convolution property of the DPRT to impose further constraints on the restoration process to increase the rate of convergence. The transformed image is then reconstructed using the inverse DPRT algorithm. We further propose in this paper a new inverse DPRT algorithm. The new algorithm collects the redundancy in the previous inverse DPRT algorithm and represents them by a filtering operation. It is then embedded into the restoration process such that it needs not be actually performed. As a result, the proposed approach reduces the iteration time by more than 50% as compared with the traditional approach to restore an image with the same quality.