Super- resolution: Warp Matrix
If H is representation of shift invariant operator then its a convolution operator. If you are implementing your algorithm in MATLAB, there is a intrinsic function with name convmtx2 which exactly do what you want.

Algorithms which warp image don't use a linear operator (a matrix) to do the job (considering large size of this operator it's not practical, even it was practical it's not an efficient method). They usually find the coordinates of warped image which generally don't match the pixel coordinates of original image then obtain pixel values using some interpolation method like nearest neighbor or bi-linear to obtain the pixel value from its neighbors.

If you want to do it by using a linear operator you have to choose an interpolation method then find the transformed coordinates and compare them to the original coordinates, then find the pixel weights regarding the interpolation method and store these weights in their corresponding location in the matrix (in nearest neighbor method give weight 1 for the nearest pixel and zero for others, in bi-linear method 4 non-zero weights for 4 pixel which are around the transformed coordinate and zero for other pixels).

Good luck.