Typical neuroimaging studies place great emphasis on not only the estimation but also the standard error estimates of underlying parameters derived from a temporal model. This is principally done to facilitate the use of t-statistics. Due to the spatial correlations in the data, it can often be more advantageous to interrogate models in the wavelet domain than in the image domain. However, widespread acceptance of these wavelet techniques has been hampered due to the limited ability to generate both parametric and error estimates in the image domain from these temporal models in the wavelet domain, without which comparison to current standard non-wavelet methods can prove difficult. This paper introduces a derivation of these estimates and an implementation for their calculation from these models for a class of thresholding estimators which have been shown to be useful for neuroimaging studies. This work stems from a consideration of the wavelet operator as a multidimensional linear operator and builds on work from the image processing community.

Date Published: 13 November 2003
PDF: 9 pages
Proc. SPIE 5207, Wavelets: Applications in Signal and Image Processing X, (13 November 2003); doi: 10.1117/12.506118

Published in SPIE Proceedings Vol. 5207:
Wavelets: Applications in Signal and Image Processing X
Michael A. Unser; Akram Aldroubi; Andrew F. Laine, Editor(s)