# Scalable Online Convolutional Sparse Coding

## TL;DR

This paper introduces an online convolutional sparse coding algorithm that significantly improves scalability and efficiency for large datasets by reformulating the problem in the frequency domain and using ADMM, enabling faster convergence and handling more data.

## Contribution

It presents a novel online learning approach for CSC that reduces computational costs and memory usage, allowing application to much larger datasets than previous batch methods.

## Key findings

- Faster convergence compared to existing methods.
- Better reconstruction performance.
- Can process at least ten times more images than prior algorithms.

## Abstract

Convolutional sparse coding (CSC) improves sparse coding by learning a shift-invariant dictionary from the data. However, existing CSC algorithms operate in the batch mode and are expensive, in terms of both space and time, on large datasets. In this paper, we alleviate these problems by using online learning. The key is a reformulation of the CSC objective so that convolution can be handled easily in the frequency domain and much smaller history matrices are needed. We use the alternating direction method of multipliers (ADMM) to solve the resulting optimization problem and the ADMM subproblems have efficient closed-form solutions. Theoretical analysis shows that the learned dictionary converges to a stationary point of the optimization problem. Extensive experiments show that convergence of the proposed method is much faster and its reconstruction performance is also better. Moreover, while existing CSC algorithms can only run on a small number of images, the proposed method can handle at least ten times more images.