Institute of Information Theory and Automation

Publication details

Fast convolutional sparse coding using matrix inversion lemma

Journal Article

Šorel Michal, Šroubek Filip

serial: Digital Signal Processing vol.55, 1 (2016), p. 44-51

project(s): GA13-29225S, GA ČR

keywords: Convolutional sparse coding, Feature learning, Deconvolution networks, Shift-invariant sparse coding

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abstract (eng):

Convolutional sparse coding is an interesting alternative to standard sparse coding in modeling shift-invariant signals, giving impressive results for example in unsupervised learning of visual features. In state-of-the-art methods, the most time-consuming parts include inversion of a linear operator related to convolution. In this article we show how these inversions can be computed non-iteratively in the Fourier domain using the matrix inversion lemma. This greatly speeds up computation and makes convolutional sparse coding computationally feasible even for large problems. The algorithm is derived in three variants, one of them especially suitable for parallel implementation. We demonstrate algorithms on two-dimensional image data but all results hold for signals of arbitrary dimension.


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Institute of Information Theory and Automation