This is a Matlab code for convolutional sparse coding, implementing the method proposed in

Michal Sorel, Filip Sroubek, "Fast convolutional sparse coding using matrix inversion lemma", Digital Signal Processing, vol. 55, pp. 44-51, 2016 (http:https://www.sciencedirect.com/science/article/pii/S1051200416300276)

Convolutional sparse coding is an alternative to standard sparse coding better suited for modelling shift-invariant signals. The most time-consuming part of both kernel learning and feature extraction is the inversion of a certain linear operator related to convolution. In this work we show how these inversions can be computed non-iteratively in the Fourier domain using the matrix inversion lemma even for multiple training signals. This greatly speeds up computation and makes convolutional sparse coding computationally feasible even for large problems.

The matrix inversion lemma to speed up the convolutional sparse coding was already independently used in recent papers of B. Wohlberg and Heide et al. (see bellow) The main problem of these methods is that they work efficiently only with one input image. In practice we would like the kernels to represent well not one particular signal/image but a set of examples. The main advantage of the proposed method is that it is fast even in such cases.

For a more detailed description see http:https://zoi.utia.cas.cz/convsparsecoding or the paper itself.

Files

example_trainkernels.m - example of training kernels

example_featureextraction.m - example of computing feature maps, once kernels are trained

convsparseF.m - main function implementing several variants of the proposed algorithm and our implementation of other methods (for details, see help included in the file). The code is implemented for 2D model, i.e. for 2D convolutions. The algorithm should work in any dimension but this code implements only the 2D variant. It can be probably used for 1D signals but not for 3D convolutions.

• 3D variant of the proposed algorithm (method = -1). Note that the name "3D" relates to how the algorithm works. This code does not work with 3D input data.
• Consensus variant of the proposed algorithm (method = -3)
• Tiling variant of the proposed algorithm (method = -4)
• M.D. Zeiler, D. Krishnan, G.W. Taylor, R. Fergus, "Deconvolutional networks", 2010 (method = 3)
• H. Bristow, A. Eriksson, S. Lucey, "Fast convolutional sparse coding", 2013 (method = 1 and method = 2)
• B. Wohlberg, "Efficient Algorithms for Convolutional Sparse Representations", 2016 (method = 0)

out_mesto_4.mat - data used as input images for learning kernels (images of Prague Old Town and Prague Castle). They are stored as a 4D array.

exp_feature_learning_E2time.m comparison of convergence for the proposed algorithm and two older algorithms

exp_feature_learning_convergence_f.m kernel learning experiment for multi-scale kernels.

Terms of Use

This code can be freely used for research purposes by academic and other non-profit organizations. If you use it in your research, please cite our paper Michal Sorel, Filip Sroubek, "Fast convolutional sparse coding using matrix inversion lemma", Digital Signal Processing, vol. 55, pp. 44-51, 2016.