Title: Abstract: I will discuss a new decomposition of the 3D X-ray transform based on the shearlet representation, a multiscale directional representation which is optimally efficient in handling 3D data containing edge singularities. This decomposition yields a highly effective reconstruction algorithm providing a near-optimal rate of convergence in estimating piecewise smooth objects from 3D...

Convolutional Neural Networks (CNNs) are a type of deep neural network which have performed well at image and audio classification. One approach to understanding the success of CNNs is Mallat’s scattering transform, which formalizes the observation that the filters learned by a CNN have wavelet-like structure. The resulting transform generates a representation that is approximately translation ...

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...

This note is concerned with the generalization of the continuous shearlet transform to higher dimensions. Quite recently, a first approach has been derived in [4]. We present an alternative version which deviates from [4] mainly by a different generalization of the shear component. It turns out that the resulting integral transform is again associated with a square-integrable group representation.

It is a challenging task to reconstruct images from their noisy, blurry, and/or incomplete measurements, especially those with important details and features such as medical magnetic resonance (MR) and CT images. We propose a novel regularization model that integrates two recently developed regularization tools: total generalized variation (TGV) by Bredies, Kunisch, and Pock; and shearlet trans...

In allusion to remove Racian noise while lessen the loss of details as low as possible, this paper proposed an filter algorithm which comprehensive utilize Multi-Objective Genetic Algorithm (MOGA) and Shearlet transform based on a Multi-scale Geometric Analysis (MGA) theory. First, it performs a wavelet multi-scale decomposition of image. Then, it builds target function in MOGA by several evalu...

Edges and surface boundaries are often the most relevant features in images and multidimensional data. It is well known that multiscale methods including wavelets and their more sophisticated multidimensional siblings offer a powerful tool for the analysis and detection of such sets. Among such methods, the continuous shearlet transform has been especially successful. This method combines aniso...