  We address the multi-focus image fusion problem, where multiple images
captured with different focal settings are to be fused into an all-in-focus
image of higher quality. Algorithms for this problem necessarily admit the
source image characteristics along with focused and blurred features. However,
most sparsity-based approaches use a single dictionary in focused feature space
to describe multi-focus images, and ignore the representations in blurred
feature space. We propose a multi-focus image fusion approach based on sparse
representation using a coupled dictionary. It exploits the observations that
the patches from a given training set can be sparsely represented by a couple
of overcomplete dictionaries related to the focused and blurred categories of
images and that a sparse approximation based on such coupled dictionary leads
to a more flexible and therefore better fusion strategy than the one based on
just selecting the sparsest representation in the original image estimate. In
addition, to improve the fusion performance, we employ a coupled dictionary
learning approach that enforces pairwise correlation between atoms of
dictionaries learned to represent the focused and blurred feature spaces. We
also discuss the advantages of the fusion approach based on coupled dictionary
learning, and present efficient algorithms for fusion based on coupled
dictionary learning. Extensive experimental comparisons with state-of-the-art
multi-focus image fusion algorithms validate the effectiveness of the proposed
approach.
