TY - GEN
T1 - Fast convolutional sparse coding with separable filters
AU - Silva, Gustavo
AU - Quesada, Jorge
AU - Rodríguez, Paul
AU - Wohlberg, Brendt
N1 - Publisher Copyright:
© 2017 IEEE.
PY - 2017/6/16
Y1 - 2017/6/16
N2 - Convolutional sparse representations (CSR) of images are receiving increasing attention as an alternative to the usual independent patch-wise application of standard sparse representations. For CSR the dictionary is a filter bank of non-separable 2D filters, and the representation itself can be viewed as the synthesis dual of the analysis representation provided by a single level of a convolutional neural network (CNN). The current state-of-the-art convolutional sparse coding (CSC) algorithms achieve their computational efficiency by applying the convolutions in the frequency domain. It has been shown that any given 2D non-separable filter bank can be approximated as a linear combination of a relatively small number of separable filters. This approximation has been exploited for computationally efficient CNN implementations, but has thus far not been considered for convolutional sparse coding. In this paper we propose a computationally efficient algorithm, that apply the convolution in the spatial domain, to solve the CSC problem when the corresponding dictionary filters are separable. Our algorithm, based on the ISTA framework, use a two-term penalty function to attain competitive results when compared to the state-of-the-art methods in terms of computational performance, sparsity and reconstruction quality.
AB - Convolutional sparse representations (CSR) of images are receiving increasing attention as an alternative to the usual independent patch-wise application of standard sparse representations. For CSR the dictionary is a filter bank of non-separable 2D filters, and the representation itself can be viewed as the synthesis dual of the analysis representation provided by a single level of a convolutional neural network (CNN). The current state-of-the-art convolutional sparse coding (CSC) algorithms achieve their computational efficiency by applying the convolutions in the frequency domain. It has been shown that any given 2D non-separable filter bank can be approximated as a linear combination of a relatively small number of separable filters. This approximation has been exploited for computationally efficient CNN implementations, but has thus far not been considered for convolutional sparse coding. In this paper we propose a computationally efficient algorithm, that apply the convolution in the spatial domain, to solve the CSC problem when the corresponding dictionary filters are separable. Our algorithm, based on the ISTA framework, use a two-term penalty function to attain competitive results when compared to the state-of-the-art methods in terms of computational performance, sparsity and reconstruction quality.
KW - Convolutional Sparse Coding
KW - Convolutional Sparse Representation
KW - Separable Filters
UR - http://www.scopus.com/inward/record.url?scp=85016265714&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2017.7953315
DO - 10.1109/ICASSP.2017.7953315
M3 - Conference contribution
AN - SCOPUS:85016265714
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 6035
EP - 6039
BT - 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017
Y2 - 5 March 2017 through 9 March 2017
ER -