INK-SVD: Learning incoherent dictionaries for sparse representations

This work considers the problem of learning an incoherent dictionary that is both adapted to a set of training data and incoherent so that existing sparse approximation algorithms can recover the sparsest representation. A new decorrelation method is presented that computes a fixed coherence dictionary close to a given dictionary. That step iterates pairwise decorrelations of atoms in the dictionary. Dictionary learning is then performed by adding this decorrelation method as an intermediate step in the K-SVD learning algorithm. The proposed algorithm INK-SVD is tested on musical data and compared to another existing decorrelation method. INK-SVD can compute a dictionary that approximates the training data as well as K-SVD while decreasing the coherence from 0.6 to 0.2.