Optimization of image interpolation as an inverse problem using the LMMSE algorithm

In this paper, a linear minimum mean square error (LMMSE) solution to the image interpolation problem is presented. The image interpolation problem is treated as an inverse problem considering the mathematical model by which a low resolution image is obtained from a high resolution image. In the suggested LMMSE (optimum) image interpolation algorithm, three main problems are encountered and solved. The autocorrelation matrix of the high resolution image is required prior to the interpolation process. This matrix is approximated from a polynomial based interpolated image and the sensitivity of the LMMSE solution to the estimation of the autocorrelation matrix is studied. Another problem is the noise variance estimation of the low resolution image. The sensitivity of the LMMSE solution to the noise variance estimation is also studied. The third problem is the large dimension matrix inversion process required for evaluating the high resolution image. This problem is solved by approximating the matrix to be inverted by a sparse matrix. Results show that the suggested solution is superior to polynomial based image interpolation algorithms from the mean square error (MSE) point of view. It is also efficient from the computational complexity point of view.