Regularized compression of a noisy blurred image

Both regularization and compression are important issues in image processing and have been widely approached in the literature. The usual procedure to obtain the compression of an image given through a noisy blur requires two steps: first a deblurring step of the image and then a factorization step of the regularized image to get an approximation in terms of low rank nonnegative factors. We examine here the possibility of swapping the two steps by deblurring directly the noisy factors or partially denoised factors. The experimentation shows that in this way images with comparable regularized compression can be obtained with a lower computational cost.