Structured and incoherent parametric dictionary design

A new dictionary selection approach for sparse coding, called parametric dictionary design, has recently been introduced. The aim is to choose a dictionary from a class of admissible dictionaries which can be presented parametrically. The designed dictionary satisfies a constraint, here the incoherence property, which can help conventional sparse coding methods to find sparser solutions in average. In this paper, an extra constraint will be applied on the parametric dictionaries to find a structured dictionary. Various structures can be imposed on dictionaries to promote a correlation between the atoms. We intentionally choose a structure to implement the dictionary using a set of filter banks. This indeed helps to implement the dictionary-signal multiplications more efficiently. The price we pay for the extra structure is that the designed dictionary is not as incoherent as unstructured parametric designed dictionaries.