Designing dictionaries to better fit the above model can be done by either selecting one from a prespecified set of linear transforms or adapting the dictionary to a set of training signals. Both of these techniques have been considered, but this topic is largely still open. In this paper we propose a novel algorithm for adapting dictionaries in order to achieve sparse signal representations. Given a set of training signals, we seek the dictionary that leads to the best representation for each member in this set, under strict sparsity constraints. We present a new method-the K-SVD algorithm-generalizing the K-means clustering process. K-SVD is an iterative method that alternates between sparse coding of the examples based on the current dictionary and a process of updating the dictionary atoms to better fit the data. The update of the dictionary columns is combined with an update of the sparse representations, thereby accelerating convergence.

http://dl.acm.org/citation.cfm?id=2201437&preflayout=flat

We developed a sparse non-negative matrix factorization (NMF) method with l0-sparseness constraints. This is similar in spirit to K-SVD but includes non-negativity constraints. Since images are naturally non-negative, this might be a direction to go for denoising.

There is a non-negative version of K-SVD too, which is, however, rather ad hoc and works slightly worse than our method. The full paper and Matlab code is provided on my profile.

Thanks U chin-Chang

Is Dictionary learning have any role in Adaptive Signal Processing?