Event Details
The role of the coarsest resolution subband in the Haar wavelet-based reconstruction of signals from gradients
Presenter: Ioana Sevcenco
Supervisor:
Date: Fri, June 29, 2018
Time: 11:00:00 - 00:00:00
Place: EOW 230
ABSTRACT
Abstract:
An efficient wavelet-based algorithm to reconstruct non-square (or
non-cubic)
signals from gradient data (first order derivatives) is developed, motivated by applications such as image or video processing in the gradient domain.
Essential to the algorithm is the relation between the gradient components and the Haar wavelet analysis high-pass filter. As such, a first step of the algorithm is to obtain the Haar wavelet decomposition of the signal, from the gradient data. Then, the signal is reconstructed using Haar wavelet synthesis.
Previous approaches typically handle the case of signals with non-square (or non-cubic) regions of support by performing some sort of extension to the nearest square (or cube).
For such a signal, the coarsest resolution subband coefficient of the Haar wavelet decomposition is easily derived from the mean value of the signal. We propose generating a non-square (or non-cubic) wavelet decomposition of the signal from the given gradient, without extending the gradient data. The challenge comes from finding the coarsest resolution subband of the wavelet decomposition and an algorithm to find this subband is proposed.
The performance of the algorithm is evaluated in terms of accuracy and computation time, and experiments show that it outperforms earlier approaches, particularly when there is a large imbalance between the signal dimensions. In addition, a closer look at the role of the coarsest resolution subband coefficients on the quality of the reconstructed signal shows that the proposed algorithm can be used in image and video processing applications.