Enhancing Boundary-Handling Strategies for Convolutional Sparse Representation Model with 46 × 46 Convolution-Multiplication Properties

Abstract

Convolutional sparse representation (CSR) extends the standard form by incorporating convolutional operations and has achieved notable success in image processing applications, offering a shift-invariant representation model. Recent studies typically redesign the initial model by exploiting the convolution-multiplication property of the discrete Fourier transform to solve the involved convex optimizations efficiently, which imposes periodic boundary handling and risks introducing boundary artifacts. This paper generalizes this approach by leveraging 46 × 46 convolution-multiplication properties while requiring only extra element-wise operations, enabling model designs that combine periodic, antiperiodic, and 40 symmetric boundary handlings for each dimension and across convolutions. These newly accepted models demonstrated better representation performance than the conventional model in our experiments, indicating the benefits of selecting appropriate boundary handlings.