A wavelet with composite dilations is a function generating an orthonormal basis or a Parseval frame for L2(Rn) under the action of lattice translations and dilations by products of elements drawn from non-commuting matrix sets A and B. Typically, the members of B are shear matrices (all eigenvalues are one) while the members of A are matrices expanding or contracting on a proper subspace of Rn...

The tunable Q-factor wavelet transform (TQWT) is a fully-discrete wavelet transform for which the Q-factor, Q, of the underlying wavelet and the asymptotic redundancy (over-sampling rate), r, of the transform are easily and independently specified. In particular, the specified parameters Q and r can be real-valued. Therefore, by tuning Q, the oscillatory behavior of the wavelet can be chosen to...

In this paper we show that the shearlets, an affine-like system of functions recently introduced by the authors and their collaborators, are essentially optimal in representing 2–dimensional functions f that are C2 except for discontinuities along C2 curves. More specifically, if fS N is the N–term reconstruction of f obtained by using the N largest coefficients in the shearlet representation, ...

This paper investigates the Parseval relationship of samples associated with the fractional Fourier transform. Firstly, the Parseval relationship for uniform samples of band-limited signal is obtained. Then, the relationship is extended to a general set of nonuniform samples of band-limited signal associated with the fractional Fourier transform. Finally, the two dimensional case is investigate...

This paper presents a thorough examination of the validity of three evaluation measures on parser output. We assess parser performance of an unlexicalised probabilistic parser trained on two German treebanks with different annotation schemes and evaluate parsing results using the PARSEVAL metric, the Leaf-Ancestor metric and a dependency-based evaluation. We reject the claim that the TüBa-D/Z a...