Non-local Sparse Models for Image Restoration Julien Mairal, Francis Bach, Jean Ponce, Guillermo Sapiro and Andrew Zisserman ICCV 2009 Presented by: Mingyuan Zhou Duke University, ECE April 09, 2010

Image restoration Two different approaches to image restoration: Dictionary learning for sparse image representation: decomposing each image patch into a linear combination of a few elements from a basis set (dictionary). Non-local means approach: explicitly exploiting the self- similarities of natural images. Simultaneous sparse coding is proposed as a framework for combining these two approaches in a natural manner, achieved by Jointly decomposing groups of similar signals on subsets of the learned dictionary. It imposes that similar patches share the same dictionary elements in their sparse decomposition.

Representative approaches Non-local Mean Sparse coding Dictionary learning

Dictionary Learning

BM3D Reference: K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3D transform-domain collaborative filtering,” IEEE Trans. Image Process., vol. 16, no. 8, pp , August 2007.

Simultaneous Sparse Coding Sparse coding is too flexible: similar patches sometimes admit very different estimates due to the potential instability of sparse decompositions Constraint: forcing similar patches to admit similar decompositions

Practical Formulation and Implementation

Demosaicking This is a file from the Wikimedia Commons.Wikimedia Commons

Denoising SC: sparse coding, use the online dictionary learning approach to train a global dictionary from 2 × 10^7 natural image patches. LSC: learned sparse coding LSSC: learned simultaneous sparse coding

Denoising

Demosaicking

Denoising + Demosaicking