Robust optimal post-filter in oversampled lapped transform: Theory and application in image coding

• We propose a method to design the optimal post-filter for TDOLTs.
• We propose a method to design the optimal post-filter for partial TDOLTs.
• We study the worst-case design of post-filter for unknown noises.
• We apply the optimal post-filter to image coding.

Time domain oversampled lapped transforms (TDOLTs) with lattice structure can guarantee linear phase and perfect reconstruction and have the advantage of improving coding efficiency and reducing blocking effects which usually exist in DCT transforms. The post-filter is not unique in TDOLTs for a fixed pre-filter. In this paper, we propose a method to design the optimal post-filter for TDOLTs and partial TDOLTs with known noises. We also study the worst-case design of post-filters when the spectrum of noises are unknown. The obtained optimal post-filter is applied to JPEG codec. The performance in reducing the blocking artifacts and effectiveness of the proposed methods are demonstrated by various examples.