Representation Learning via Cauchy Convolutional Sparse Coding
This is an incremental improvement for researchers in unsupervised learning and image processing, focusing on enhancing reconstruction quality in natural images.
The paper tackles the problem of improving image reconstruction in unsupervised representation learning by proposing a Cauchy prior-based regularization for Convolutional Sparse Coding, resulting in an Iterative Cauchy Thresholding algorithm that outperforms existing methods with average PSNR gains of up to 11.30 and 7.04 over ISTA and IHT.
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 a regularisation term derived from an assumed Cauchy prior for the coefficients of the feature maps of a CSC generative model. The sparsity penalty term resulting from this prior is solved via its proximal operator, which is then applied iteratively, element-wise, on the coefficients of the feature maps to optimise the CSC cost function. The performance of the proposed Iterative Cauchy Thresholding (ICT) algorithm in reconstructing natural images is compared against the common choice of \(\ell_1\)-norm optimised via soft and hard thresholding. ICT outperforms IHT and IST in most of these reconstruction experiments across various datasets, with an average PSNR of up to 11.30 and 7.04 above ISTA and IHT respectively.