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

A new approach for regularized image interpolation

“…Here M=N/R, where R is the ratio between the sizes of f(n 1 ,n 2 ) and g(m 1 ,m 2 ) . The relationship between the LR image and the HR image can be represented by the following mathematical model [19][20][21][22]:…”

“…Unfortunately, the estimation of this correction filter in our case is difficult or even impossible. This is because our problem represented by equation (1) is an illposed inverse problem [19][20][21][22]. The treatment of ill-posed inverse problem in the presence of noise is performed using different techniques such as regularization techniques and Wiener filtering techniques [18].…”

“…In CCD imaging, there is an interaction between the adjacent points in the object to be imaged to form a pixel in the obtained image [19][20][21][22]. If this model of interaction is considered in image interpolation, the interpolation process will be similar to a process of imaging with an HR imaging device to a great extent and better results are expected to occur.…”

“…Some image interpolation algorithms have been introduced considering this interaction process [19][20][21][22]. The linear minimum mean square error (LMMSE) image interpolation algorithm is one of them [19,21].…”

“…The linear minimum mean square error (LMMSE) image interpolation algorithm is one of them [19,21]. Another one is the regularized image interpolation algorithm.…”