Spatially adaptive interpolation and super-resolution using the optimal recovery framework
Reconstruction of missing pixels from the available Low Resolution (LR) Image pixels in order to create a High Resolution (HR) Image is a very important problem with many applications. In our research, we propose a spatially adaptive optimal recovery interpolation method for generating a discrete High Resolution Image from any given discrete Low resolution Image. This Spatially Adaptive OR approach is then extended to Super-Resolution technique. Optimal Recovery (OR) method can be used for reconstructing signals from uniform samples. The OR framework uses the values of a given linear operator to estimate the value of a desired linear operator. The OR method is capable of incorporating bandwidth or spectral shape information and a regularization parameter in the reconstruction process. Depending upon the spectral support function used, in order to achieve stability from noise or the linear inverse problem in the reconstruction process a regularization parameter must be used. Generalized Cross Validation (GCV) approach has been proposed to find an optimal regularization parameter in underdetermined problems. Instead of taking a single regularization parameter for the whole image we calculate the regularization parameter for each block of the image which will take local properties of an image into consideration. The bandwidth information is also adapted based on the statistics of each corresponding block from the LR image. Examples and comparisons with other interpolation methods are included. Adaptively varying the bandwidth information and incorporation of regularization parameter based on the local characteristics of the LR image are two important characteristics in the OR based Interpolation. We implemented this adaptive interpolation technique in two ways- block wise reconstruction without overlapping and block wise reconstruction with overlapping. Multi-frame image restoration or Super-Resolution (SR) is the process of combining multiple low resolution images in order to reconstruct a single high resolution image. SR first involves registration of multiple images or frames and from the obtained registration information, a high resolution image is generated from the shifted LR images. The Spatially Adaptive Super-Resolution based on the optimal recovery framework is developed here for a limited scope of the full SR problem. It assumes the registration information is already available and does not incorporate any deconvolution. The bandwidth information and the regularization parameter are calculated adaptively as mentioned above but we use the information from all the LR images which corresponds to the non-uniform interpolation. Simulations show the benefit of the adaptive scheme over fixed optimal recovery based super-resolution and is compared with other methods as well.
Shaik, Abdul Jabeer, "Spatially adaptive interpolation and super-resolution using the optimal recovery framework" (2012). ETD Collection for University of Texas, El Paso. AAI1512632.