The shearlet representation has gained increasing recognition in recent years as a framework for the efficient representation of multidimensional data. This representation consists of a countable collection of functions defined at various locations, scales and orientations, where the orientations are obtained through the use of shearing matrices. While shearing matrices offer the advantage of p...

This paper investigates the efficiency of unbalanced versus balanced multiwavelets in stereo correspondence matching. A multiwavelet transform is first applied to a pair of stereo images to decorrelate them into a number of subbands. Information in the approximation subbands of an unbalanced multiwavelet carries different spectral content of the input image while the balanced multiwavelet appro...

Vector wavelet transforms for vector-valued fields can be implemented directly from multiwavelets; however, existing multiwavelets offer surprisingly poor performance for transforms in vector-valued signal-processing applications. In this paper, the reason for this performance failure is identified, and a remedy is proposed. A multiwavelet design criterion, omnidirectional balancing, is introdu...

There are perfect construction formulas for the orthonormal uniwavelet. However, it seems that there is not such a good formula with similar structure for multiwavelets. Especially, construction of multiwavelets with dilation factor a(a ≥ 2, a ∈ Z) lacks effective methods. In this paper, a procedure for constructing compactly supported orthonormal multiscale functions is first given, and then b...

Background Sub-millimeter resolution, background-free magnetic resonance angiography (MRA) has been performed previously using dynamic nuclear polarization (DNP)enhanced C labeled small molecules [1-4]. This approach of contrast-enhanced MRA is appealing since many of the commonly used DNP substrates are endogenous and could be potentially used in large doses in patients with renal insufficienc...

We introduce Parseval networks, a form of deep neural networks in which the Lipschitz constant of linear, convolutional and aggregation layers is constrained to be smaller than 1. Parseval networks are empirically and theoretically motivated by an analysis of the robustness of the predictions made by deep neural networks when their input is subject to an adversarial perturbation. The most impor...

Introduction: The term Subclavian steal refers to reversal of normal direction of flow in the vertebral artery ipsilateral to severe stenosis/occlusion occurring between aortic arch and vertebral artery origin. The diagnosis of subclavian steal syndrome can be suggested by many techniques which include invasive angiography, noninvasive continuous wave Doppler ultrasonography of neck, multi-slic...

In this dissertation, we study the structure of correlation minimizing frames. A correlation minimizing (N,d)-frame is any uniform Parseval frame of N vectors in dimension, d, such that the largest absolute value of the inner products of any pair of vectors is as small as possible. We call this value the correlation constant. These frames are important as they are optimal for the 2-erasures pro...

The developments in wavelet theory have given rise to the wavelet thresholding method, for extracting a signal from noisy data [1,2]. Multiwavelets, wavelets with several scaling functions, have recently been introduced and they offer simultaneous orthogonality, symmetry and short support; which is not possible with ordinary wavelets, also called scalar wavelets [3]. This property makes multiwa...