Dictionary Learning of Binary Atoms by using a Smooth Approximation

The decomposition of a signal as a linear combination of few atoms of a learned dictionary has been widely studied for low and high-level tasks in signal and image processing applications. The atoms of the dictionary are typically assumed to be normalized, real-valued, and stored as floating-point numbers, which leads to high costs in storage and transmission time for large scale applications. In this work, we propose to learn binary atoms in order to represent an image sparsely. To solve this problem, we include a smoothing function for binarization and present an algorithm that iteratively alternates between a sparse coding update and a dictionary update. The binary structure allows to reduce the storage size of the dictionary as well as efficiently synthesize the underlying image using only addition and subtraction operations. Experiments on sparse representation of natural images show that the proposed binary dictionary gains up to 2 dB compared to binary dictionaries obtained using traditional binarization techniques.