Representation Learning via Cauchy Convolutional Sparse Coding

In representation learning, Convolutional Sparse Coding (CSC) enables unsupervised learning of features by jointly optimising both an $\ell _{2}$ -norm fidelity term and a sparsity enforcing penalty. This work investigates using regularisation derived from assumed Cauchy prior for the coefficients feature maps CSC generative model. The penalty resulting this is solved via its proximal operator, which then applied iteratively, element-wise, on to optimise cost function. performance proposed Iterative Thresholding (ICT) algorithm in reconstructing natural images compared against algorithms based minimising standard functions soft hard thresholding as well Log-Thresholding (ILT) method. ICT outperforms Hard (IHT), Soft (IST), ILT most our reconstruction experiments across various datasets, with average Peak Signal Noise Ratio (PSNR) up 11.30 dB, 7.04 7.74 dB over IST, IHT, respectively. source code implementation approach publicly available at https://github.com/p-mayo/cauchycsc