A multilayered convolutional sparse coding framework for modeling of pooling operation of convolution neural networks

Convolutional Sparse Coding (CSC) framework has been proposed recently to explain relation between Convolutional Neural Networks (CNNs) and sparse coding theory. The multilayered version of CSC(ML-CSC) is shown to be connected to forward pass of CNNs and dictionary learning and sparse coding algorithms of this model are analyzed for solving classification and inverse problems in image processing. However open problems like effect of pooling operations, batch normalization and dictionary learning in context of ML-CSC framework remain challenging issues especially in implementation scenarios. In this work we implement the framework for multi layered version of CSC with incorporation of pooling operations applied on real images and analyze the performance of resulting model. We demonstrate that with optimal parameters selected for sparsity of feature maps, the pooling operation (here max pooling) when used layered wise in ML-CSC framework improves the effective dictionaries and resulting feature maps, which in turn improves the reconstruction accuracy of images after multilayered implementation