This paper introduces a Parseval frame of shearlets for the representation of 3D data, which is especially designed to handle geometric features such as discontinuous boundaries with very high efficiency. This system of 3D shearlets forms a multiscale pyramid of well-localized waveforms at various locations and orientations, which become increasingly thin and elongated at fine scales. We prove ...

In this paper, we first briefly review the directional properties of the Dual-Tree complex wavelet transform and we investigate how the directional selectivity of the transform can be increased (i.e., to obtain more than 6 orientations per scale). To this end, we describe a new augmented Lagrangian optimization algorithm to jointly perform the 2D spectral factorization of a set of 2D directiona...

The fast digital shearlet transform (FDST) was recently introduced as a means to analyze natural images efficiently, owing to the fact that those are typically governed by cartoon-like structures. In this paper, we introduce and discuss a first-order hybrid sigma-delta quantization algorithm for coarsely quantizing the shearlet coefficients generated by the FDST. Radial oversampling in the freq...

To reduce the x-ray dose in computerized tomography (CT), many constrained optimization approaches have been proposed aiming at minimizing a regularizing function that measures lack of consistency with some prior knowledge about the object that is being imaged, subject to a (predetermined) level of consistency with the detected attenuation of x-rays. One commonly investigated regularizing funct...

The predictive power of top–condensation models strongly depends on the behaviour of higher dimensional operators. These are analyzed in this paper by an extension of the standard renormalization group (RG) arguments which turns out to be a surprisingly powerful tool. Top–condensation models intermediated by underlying scalar exchange can be shown to be mere reparametrizations of the standard m...