Simple Signal Extension Method for Discrete Wavelet Transform

TL;DR

This paper introduces a simple, efficient signal extension method for the discrete wavelet transform that simplifies boundary handling, reduces processing complexity, and enables immediate output without buffering, especially in multi-scale image coding.

Contribution

It proposes a compact streaming core for boundary treatment in DWT, specifically for CDF 5/3 wavelet, improving efficiency over complex traditional methods.

Findings

Each input sample is visited only once.

Results are produced immediately without buffering.

Applicable to multi-scale image decomposition in JPEG 2000.

Abstract

Discrete wavelet transform of finite-length signals must necessarily handle the signal boundaries. The state-of-the-art approaches treat such boundaries in a complicated and inflexible way, using special prolog or epilog phases. This holds true in particular for images decomposed into a number of scales, exemplary in JPEG 2000 coding system. In this paper, the state-of-the-art approaches are extended to perform the treatment using a compact streaming core, possibly in multi-scale fashion. We present the core focused on CDF 5/3 wavelet and the symmetric border extension method, both employed in the JPEG 2000. As a result of our work, every input sample is visited only once, while the results are produced immediately, i.e. without buffering.