A fast atom selection method based on the order of initial inner product values for image denoising using sparse representation

In sparse representation, each patch of an image is represented as a linear combination of a few atoms, chosen from an overcomplete basis dictionary. The standard sparse representation requires much computation for inner products to select atoms from a dictionary and for pseudoinverse matrix calculation to determine sparse coefficients. Considering future popularization of high-resolution images, this computational complexity must be reduced. In this paper, we propose a fast atom selection method for sparse representation based on the order of the inner product values between an image patch and the atoms in an overcomplete basis dictionary. The proposed method reduces both the number of the inner product to less than 50.0% and the number of coefficient optimization to 37.7% without subjective image quality degradation when compared to the OMP method.