Robust transform learning

Dictionary learning follows a synthesis framework; the dictionary is learnt such that the data can be synthesized / re-generated from the coefficients. Transform learning on the other hand is based on analysis formulation; it learns a transform so as to generate the coefficients. The basic formulations of dictionary learning and transform learning employ a Euclidean cost function for the data fidelity term. Such cost functions are optimal when the noise / error in the system is Normally distributed, but not in the presence of sparse but large outliers. For such heavy tailed noise distributions, minimizing the absolute distance is more robust. There are several papers on robust dictionary learning. This work introduces robust transform learning. Experiments carried out on image analysis and impulse denoising elucidate the superiority of our method.