Refine
Year of publication
- 2013 (1)
Document Type
- Preprint (1)
Language
- English (1) (remove)
Has Fulltext
- yes (1)
Keywords
- Riesz Transform (1)
- Shearlets (1)
- instantaneous phase (1)
- local orientation (1)
- monogenic signals (1)
Faculty / Organisational entity
The only quadrature operator of order two on \(L_2 (\mathbb{R}^2)\) which covaries with orthogonal
transforms, in particular rotations is (up to the sign) the Riesz transform. This property
was used for the construction of monogenic wavelets and curvelets. Recently, shearlets
were applied for various signal processing tasks. Unfortunately, the Riesz transform does
not correspond with the shear operation. In this paper we propose a novel quadrature operator called linearized Riesz transform which is related to the shear operator. We prove
properties of this transform and analyze its performance versus the usual Riesz transform numerically. Furthermore, we demonstrate the relation between the corresponding
optical filters. Based on the linearized Riesz transform we introduce finite discrete quasi-monogenic shearlets and prove that they form a tight frame. Numerical experiments show
the good fit of the directional information given by the shearlets and the orientation ob-
tained from the quasi-monogenic shearlet coefficients. Finally we provide experiments on
the directional analysis of textures using our quasi-monogenic shearlets.