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Jorge Quesada, Gustavo Silva, Paul Rodríguez and Brendt Wohlberg, "Combinatorial Separable Convolutional Dictionaries", in Symposium on Image, Signal Processing and Artificial Vision (STSIVA), (Bucaramanga, Colombia), Apr 2019


Recent works have considered the use of a linear combination of separable filters to approximate a non-separable filter bank (FB) to obtain computational advantages in CNNs and convolutional sparse representations / coding (CSR / CSC). However, it has been recently shown that there are advantages to directly solving the convolutional dictionary learning (CDL) problem considering a separable FB.

A separable filter bank of M 2-d filters is typically constructed from a paired set of M horizontal filters and M vertical filters. In contrast, here we propose an outer product construction involving all possible combinations of vertical and horizontal filters, so that M vertical and M horizontal filters generate M 2 2-d filters. Our computational experiments show that this alternative form results in a reduction in computation time of 10% and 80% for the CDL and CSC problems respectively, while matching the reconstruction performance of the typical separable FB approach for the same cardinality.

BibTeX Entry

author = {Jorge Quesada and Gustavo Silva and Paul Rodr\'{i}guez and Brendt Wohlberg},
title = {Combinatorial Separable Convolutional Dictionaries},
year = {2019},
month = Apr,
urlpdf = {},
booktitle = {Symposium on Image, Signal Processing and Artificial Vision (STSIVA)},
address = {Bucaramanga, Colombia},
note = {Accepted for presentation}