A novel image denoising algorithm using linear Bayesian MAP estimation based on sparse representation

• Research sparsity prior of nature images based on sparse representation modeling.
• Establish a linear Bayesian MAP estimator with sparsity prior for inverse problem.
• Develop an approximate solution with closed-form to the MAP estimator.
• Data clustering is exploited for improving the denoising performance.

A novel image denoising algorithm using linear Bayesian maximum a posteriori (MAP) estimation based on sparse representation model is proposed. Starting from constructing prior probability distribution in representation vector, a linear Bayesian MAP estimator is constructed in order to acquire the most probable one behind the observations, which is adaptive to solve the generalized image inverse problems. Furthermore, a practical closed-form solution by affording some plausible approximations is obtained, and thus image denoising as a specialization can be easily solved. With our new method, we first extract all possible patches from noisy images and classify them to several sub-groups by their structural patterns, then train a different dictionary per each using the K-SVD algorithm, following by estimating corresponding parameters in MAP estimator. The final denoised image is obtained by applying denoising on each sub-group based on the estimator and averaging these outputs together. Simulated results show that the proposed method achieves a very competitive performance both in subjective visual quality and objective PSNR value, compared with other state-of-the-art denoising algorithms.