Optimized projections for generalized joint sparse representation based image fusion

Sparse representation (SR) and joint sparse representation (JSR) have attracted a lot of interest in image fusion. The SR models signals by sparse linear combinations of prototype signal atoms that make a dictionary. Compressed sensing (CS) has shown that sparse signals can be recovered from far less samples than those required by the classical Shannon-Nyquist Theorem. Random projections (random Gaussian, rGauss) were used since they present small coherence with almost any dictionary. However, optimizing the projection matrix toward decreasing the coherence between the projection matrix and the dictionary is possible and can improve the performance. The JSR indicates that different signals from an ensemble have a common sparse component, and each individual signal owns an innovation sparse component. The JSR offers lower computational complexity than SR does. Our previous work proposed the generalized joint sparse representation (GJSR) which the signals ensemble depends on two dictionaries. This paper gives a gradient method with Barzilai-Borwein stepsize (GBB) for the optimization of the projections in GJSR. The validity of the proposed method is illustrated by some experiments for synthesized signals and real-world image fusion.