Image Restoration by Group Sparsity with Union of Hierarchical DirLOTs

In this study, we propose to introduce group sparse regularization with multiple Directional Lapped Orthogonal Transforms (DirLOTs) for image restoration. Sparse signal restoration has shown its effectiveness in a wide variety of fields. While ℓ
₁
-norm regularization is typically used in sparse restoration, a group sparse regularization can restore signals more effectively if sparse structure in signals is organized into groups. As a previous research, a group sparse regularization with dependency between discrete wavelet transform (DWT) coefficients has been proposed and the significance is demonstrated. Since DirLOTs are redundant and symmetric, more effective sparse restoration can be expected than ordinary DWTs. In this work, we introduce group sparse regularization into image restoration with multiple DirLOTs, where the symmetric property is utilized. Through simulations, the restoration performance of the proposed method is shown and the significance is confirmed.