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

The discrete periodic Radon transform (DPRT) has many useful properties that enable a 2-D signal to be processed by 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 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 reconstructed using the inverse DPRT algorithm. We propose a new inverse DPRT algorithm, which 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 need not be actually performed. As a result, the proposed approach reduces the iteration time by more than 50%.