Convolutional Dictionary Learning via Local Processing
This work addresses limitations in convolutional sparse coding for signal and image processing, offering a more intuitive and flexible approach, though it appears incremental by building on prior theoretical analysis.
The paper tackles the problem of convolutional sparse coding by proposing a method that operates locally on image patches, enabling efficient dictionary learning and sparse pursuit. It achieves state-of-the-art results in image inpainting and image separation.
Convolutional Sparse Coding (CSC) is an increasingly popular model in the signal and image processing communities, tackling some of the limitations of traditional patch-based sparse representations. Although several works have addressed the dictionary learning problem under this model, these relied on an ADMM formulation in the Fourier domain, losing the sense of locality and the relation to the traditional patch-based sparse pursuit. A recent work suggested a novel theoretical analysis of this global model, providing guarantees that rely on a localized sparsity measure. Herein, we extend this local-global relation by showing how one can efficiently solve the convolutional sparse pursuit problem and train the filters involved, while operating locally on image patches. Our approach provides an intuitive algorithm that can leverage standard techniques from the sparse representations field. The proposed method is fast to train, simple to implement, and flexible enough that it can be easily deployed in a variety of applications. We demonstrate the proposed training scheme for image inpainting and image separation, while achieving state-of-the-art results.