Partitioned Convolutional Dictionary Learning over Imbalanced Subspaces

Sparse Coding (SC) is powerful tool for representing data in a reduced dimensionality with minimal loss of information. Sparse Dictionary Learning (SDL) is the machine learning process of improving representational features for SC. Traditional frame metrics have an underlying assumption that the distribution of the dataset's spectrum is radially symmetric. Under the assumption of a radially symmetric distribution, optimized frame metrics provide an optimal sparse representation. Real-world datasets typically aren't symmetric, to which optimized frame metrics harm the performance of sparse representations. Partitioning of a dataset into balanced spectral subspaces can approximate a breakdown of the data into more radially symmetric distributions. Partitioned Dictionary Learning (PDL) utilizes the balanced subspaces to learn incoherent dictionaries to improve sparse representations. The work of PDL serves as a basis to extend the popular Convolutional Dictionary Learning (CDL) into a Partitioned Convolutional Dictionary Learning (PCDL), where the spectral partitioning is efficient to compute.