# Interpolation by Optimization

I have the following interpolation problem:

Given an M by N channel image (1 Channel).

A certain set of pixels are defined as anchors.
The rest of the pixels should be interpolated using the original data by minimizing the follwoing cost function:

Where E is the new matrix of interpolated pixels and I is the original image.

Pay attention that the interpolated image equals the original image at the anchor pixels.

The inteprolation weights are given by:

My question is, how can I formalize it in Weighted LS form?

Any optimization could be made to solve it quickly and efficiently?

This interpolation could be used as a minimization for many application in image processing (Edge Preserving Interpolation, Colorization, etc...).

Thank You.

Anyone? It should be pretty widely used optimization problem.