High Order Tensor Formulation for Convolutional Sparse Coding

Convolutional sparse coding (CSC) has gained attention for its successful role as a reconstruction and a classification tool in the computer vision and machine learning community. Current CSC methods can only reconstruct single-feature 2D images independently. However, learning multi-dimensional dictionaries and sparse codes for the reconstruction of multi-dimensional data is very important, as it examines correlations among all the data jointly. This provides more capacity for the learned dictionaries to better reconstruct data. In this paper, we propose a generic and novel formulation for the CSC problem that can handle an arbitrary order tensor of data. Backed with experimental results, our proposed formulation can not only tackle applications that are not possible with standard CSC solvers, including colored video reconstruction (5D- tensors), but it also performs favorably in reconstruction with much fewer parameters as compared to naive extensions of standard CSC to multiple features/channels.