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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), doi:10.1109/STSIVA.2019.8730236, 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},
doi = {10.1109/STSIVA.2019.8730236}