Computationally Efficient Formulation of Sparse Color Image Recovery in the JPEG Compressed Domain

Sparse representations provide a powerful framework for various image processing tasks, among which image recovery seems to be an already classical application. While most developments of image recovery applications are focused on finding the best dictionary, the possibility of using already existing sparse image representations tends to be ignored. This is the case of the JPEG compressed image representation, which is a sparse image representation in terms of the discrete cosine transform (DCT) dictionary. The development of sparse frameworks directly on the JPEG encoded image representation can lead to computationally efficient approaches. Here we introduce a DCT-based JPEG compressed domain formulation of the color image recovery process within a sparse representation framework and we prove mathematically and experimentally not only its numerical efficiency as compared to the pixel level formulation (the processing time is reduced up to 40 %), but also the good quality of the restoration results.