3D Steerable Wavelets in Practice

Nicolas Chenouard

doi:10.1109/TIP.2012.2206044

Return

3D Steerable Wavelets in Practice

2012-11-01

Nicolas Chenouard *

Michaël Unser

DOI：10.1109/TIP.2012.2206044

Original

Original request for help

Save

Abstract

En 中文

We introduce a systematic and practical design for steerable wavelet frames in 3D. Our steerable wavelets are obtained by applying a 3D version of the generalized Riesz transform to a primary isotropic wavelet frame. The novel transform is self-reversible (tight frame) and its elementary constituents (Riesz wavelets) can be efficiently rotated in any 3D direction by forming appropriate linear combinations. Moreover, the basis functions at a given location can be linearly combined to design custom (and adaptive) steerable wavelets. The features of the proposed method are illustrated with the processing and analysis of 3D biomedical data. In particular, we show how those wavelets can be used to characterize directional patterns and to detect edges by means of a 3D monogenic analysis. We also propose a new inverse-problem formalism along with an optimization algorithm for reconstructing 3D images from a sparse set of wavelet-domain edges. The scheme results in high-quality image reconstructions which demonstrate the feature-reduction ability of the steerable wavelets as well as their potential for solving inverse problems.

Keywords:

3D wavelet transform

edge detection

image reconstruction

monogenic signal

riesz transform

steerability