ABSTRACT
Theoretical studies on dictionary learning that fit the problem into a statistical learning framework and justify the above-mentioned optimization problem are given in [23, 36, 12, 10]. In fact, in the previous framework, we minimize an empirical average over the training data, whereas the idealized task would be to optimize an expected cost function over the underlying (and unknown) distribution that generated the data. We point out that in [10] this study is pursed with general coefficient penalties and dictionary constraints, covering all the types of dictionary learning problems mentioned above.
