You can use randperm to shuffle the indices randomly, then sort to get the indices for reversing it:
% load in an image included in Matlab
corn_gray = imread('corn.tif',3);
% get the size
imsize = size(corn_gray);
% display
imshow(corn_gray)
% create a randomly-shuffled list of linear indices 1:total pixels
idx_shuffle=randperm(numel(corn_gray));
% get the inverse (idx_shuffle(idx_unshuffle) = 1:total pixels)
[~,idx_unshuffle] = sort(idx_shuffle);
% put the indices into the same row-col shape as the image
idx_shuffle = reshape(idx_shuffle,imsize);
idx_unshuffle = reshape(idx_unshuffle,imsize);
% compute the shuffled image
corn_gray_shuffled = corn_gray(idx_shuffle);
% run an arbitrary transformation on it
corn_gray_shuffled = corn_gray_shuffled.^2;
% display the shuffled, transformed image
imshow(corn_gray_shuffled)
% unshuffle the transformed image
corn_gray_unshuffled = corn_gray_shuffled(idx_unshuffle);
% and display
imshow(corn_gray_unshuffled)
