Image modeling and enhancement via structured sparse model selection

An image representation framework based on structured sparse model selection is introduced in this work. The corresponding modeling dictionary is comprised of a family of learned orthogonal bases. For an image patch, a model is first selected from this dictionary through linear approximation in a best basis, and the signal estimation is then calculated with the selected model. The model selection leads to a guaranteed near optimal denoising estimator. The degree of freedom in the model selection is equal to the number of the bases, typically about 10 for natural images, and is significantly lower than with traditional overcomplete dictionary approaches, stabilizing the representation. For an image patch of size √N × √N, the computational complexity of the proposed framework is O (N²), typically 2 to 3 orders of magnitude faster than estimation in an overcomplete dictionary. The orthogonal bases are adapted to the image of interest and are computed with a simple and fast procedure. State-of-the-art results are shown in image denoising, deblurring, and inpainting.