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In continuous-time wavelet analysis, most wavelet present some kind of symmetry. Based on the Fourier and Hartley transform kernels, a new wavelet multiresolution analysis is proposed. This approach is based on a pair of orthogonal wavelet…

Image-based rigid 2D/3D registration is a critical technique for fluoroscopic guided surgical interventions. In recent years, some learning-based fully differentiable methods have produced beneficial outcomes while the process of feature…

Microlocal analysis provides deep insight into singularity structures and is often crucial for solving inverse problems, predominately, in imaging sciences. Of particular importance is the analysis of wavefront sets and the correct…

Deep neural networks are widely used for understanding 3D point clouds. At each point convolution layer, features are computed from local neighborhoods of 3D points and combined for subsequent processing in order to extract semantic…

The data-driven sparse methods such as synthesis dictionary learning (e.g., K-SVD) and sparsifying transform learning have been proven effective in image denoising. However, they are intrinsically single-scale which can lead to suboptimal…

We propose a class of spherical wavelet bases for the analysis of geophysical models and forthe tomographic inversion of global seismic data. Its multiresolution character allows for modeling with an effective spatial resolution that varies…

Optical approaches for wavefront shaping traditionally rely on phase modulation through holographic techniques. Shaping the phase determines a wave's diffraction and hence its intensity distribution in space. We instead show that shaping…

A nearly optimal explicitly-sparse representation for oscillatory kernels is presented in this work by developing a curvelet based method. Multilevel curvelet-like functions are constructed as the transform of the original nodal basis. Then…

The bilateral filter is a useful nonlinear filter which without smoothing edges, it does spatial averaging. In the literature, the effectiveness of this method for image denoising is shown. In this paper, an extension of this method is…

We present the development of extended diffraction tomography, a new approach to the solution of the linear seismic waveform inversion problem. This method has several appealing features, such as the use of arbitrary depth-dependent…

Scalable lossless video coding is an important aspect for many professional applications. Wavelet-based video coding decomposes an input sequence into a lowpass and a highpass subband by filtering along the temporal axis. The lowpass…

We propose a convolutional neural network (CNN) architecture for image classification based on subband decomposition of the image using wavelets. The proposed architecture decomposes the input image spectra into multiple critically sampled…

Automatic synthesis of high quality 3D shapes is an ongoing and challenging area of research. While several data-driven methods have been proposed that make use of neural networks to generate 3D shapes, none of them reach the level of…

In this paper, we design mother wavelets for the 1D continuous wavelet transform with some optimality properties. An optimal mother wavelet here is one that has an ambiguity function with minimal spread in the continuous coefficient space…

Image data are often composed of two or more geometrically distinct constituents; in galaxy catalogs, for instance, one sees a mixture of pointlike structures (galaxy superclusters) and curvelike structures (filaments). It would be ideal to…

To improve diagnostic accuracy of breast cancer detection, several researchers have used the wavelet-based tools, which provide additional insight and information for aiding diagnostic decisions. The accuracy of such diagnoses, however, can…

This paper presents a novel and efficient method for characteristic mode decomposition in multi-structure systems. By leveraging the translation and rotation matrices of vector spherical wavefunctions, our approach enables the synthesis of…

The intrinsically hierarchical and blended structure of interstellar molecular clouds, plus the always increasing resolution of astronomical instruments, demand advanced and automated pattern recognition techniques for identifying and…

Kinetic energy harvesting with piezoelectric bimorphs has attracted considerable research interest in recent years. Many works have been dedicated to the modelling and optimisation of the cantilevered geometry to increase power density,…

With recent success of deep learning in 2D visual recognition, deep learning-based 3D point cloud analysis has received increasing attention from the community, especially due to the rapid development of autonomous driving technologies.…