Sparse representations using overcomplete dictionaries has concentrated mainly on the study of pursuit algorithms that decompose signals with respect to a given dictionary. 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. The K-SVD algorithm 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. However, the existing K-SVD algorithm is employed to dwell on the concept of a binary class assignment meaning that the multi-classes samples are assigned to the given classes definitely. The work proposed in this paper provides a novel fuzzy adaptive way to adapting dictionaries in order to achieve the fuzzy sparse signal representations, the update of the dictionary columns is combined with an update of the sparse representations by incorporated a new mechanism of fuzzy set, which is called fuzzy K-SVD. Experimental results conducted on the ORL and Yale face databases demonstrate the effectiveness of the proposed method.
Sparse signal representations using the tunable Q-factor wavelet transform
