  A new method is proposed in this paper to learn overcomplete dictionary from
training data samples. Differing from the current methods that enforce similar
sparsity constraint on each of the input samples, the proposed method attempts
to impose global sparsity constraint on the entire data set. This enables the
proposed method to fittingly assign the atoms of the dictionary to represent
various samples and optimally adapt to the complicated structures underlying
the entire data set. By virtue of the sparse coding and sparse PCA techniques,
a simple algorithm is designed for the implementation of the method. The
efficiency and the convergence of the proposed algorithm are also theoretically
analyzed. Based on the experimental results implemented on a series of signal
and image data sets, it is apparent that our method performs better than the
current dictionary learning methods in original dictionary recovering, input
data reconstructing, and salient data structure revealing.
