Image denoising via 2D dictionary learning and adaptive hard thresholding

• It is illustrated that there exists two-direction linear correlation in natural images.
• The two-direction linear correlations are explored for image denoising.
• The two-direction correlations are explored by the 2D dictionary learning.
• The patches are estimated by the sparse approximation with respect to the locally learned 2D dictionary.
• And the sparse approximation is implemented by the simple adaptive hard thresholding.

There is extensive interest in taking advantage of self-similarity inherent in images to learn adaptive dictionary for effective image representation and denoising in recent years. In this letter, we present a complementary view. When a group of similar patches are arranged into the so called similarity data matrix (SDM), there exist linear correlations among both columns and rows of the SDM. With this observation, we propose an image denoising algorithm based on 2D dictionary learning and adaptive hard thresholding (2DDL-AHT). In this algorithm, both row-correlation and column-correlation of the SDM are explored by 2D dictionary learning, and a group of similar patches are estimated by using adaptive hard thresholding. The experiments indicate that the proposed algorithm performs on par or slightly better than the state-of-the-art denoising methods.