相关论文: Wavelets and Information-preserving Transformation…
In a recent article [1] we have explored alternative decompositions of the Lorentz transformation by adopting the synchronization convention of the target frame at the end and alternately at the outset. In this note we develop the…
In this letter, the wavelet transform is used to decompose the classical linearly polarized plane light wave into a series of discrete Morlet wavelets. It is found that the energy of the light wave can be discrete, associated with its…
The covariance group for general relativity, the diffeomorphisms, is replaced by a group of coordinate transformations which contains the diffeomorphisms as a proper subgroup. The larger group is defined by the assumption that all observers…
Scattering in complex media scrambles light, thus obscuring images and limiting applications from astronomy to microscopy. Existing computational and wavefront-shaping methods treat scattering as a linear optical-wave inversion problem that…
The feature learning methods based on convolutional neural network (CNN) have successfully produced tremendous achievements in image classification tasks. However, the inherent noise and some other factors may weaken the effectiveness of…
Many stochastic processes are defined on special geometrical objects like spheres and cones. We describe how tools from harmonic analysis, i.e. Fourier analysis on groups, can be used to investigate probability density functions (pdfs) on…
Wavelets are a useful basis for constructing solutions of the integral and differential equations of scattering theory. Wavelet bases efficiently represent functions with smooth structures on different scales, and the matrix representation…
In this paper, some important properties of the windowed offset linear canonical transform (WOLCT) such as shift, modulation and orthogonality relation are introduced. Based on these properties we derive the convolution and correlation…
A wavelet scattering network computes a translation invariant image representation, which is stable to deformations and preserves high frequency information for classification. It cascades wavelet transform convolutions with non-linear…
In Image Compression, the researchers' aim is to reduce the number of bits required to represent an image by removing the spatial and spectral redundancies. Recently discrete wavelet transform and wavelet packet has emerged as popular…
Generating highly detailed, complex data is a long-standing and frequently considered problem in the machine learning field. However, developing detail-aware generators remains an challenging and open problem. Generative adversarial…
Invariance of the counted number of photons and the Lorentz-Einstein transformations enable us to derive transformation equations for the physical quantities introduced in order to characterize energy emission and transport in a plane and…
When Einstein formulated his special relativity, he developed his dynamics for point particles. Of course, many valiant efforts have been made to extend his relativity to rigid bodies, but this subject is forgotten in history. This is…
Cloud detection is a specialized application of image recognition and object detection using remotely sensed data. The task presents a number of challenges, including analyzing images obtained in visible, infrared and multi-spectral…
Wavelets are well known for data compression, yet have rarely been applied to the compression of neural networks. This paper shows how the fast wavelet transform can be used to compress linear layers in neural networks. Linear layers still…
Lorentz transmission electron microscopy is a unique characterization technique that enables the simultaneous imaging of both the microstructure and functional properties of materials at high spatial resolution. The quantitative information…
This note introduces a new family of wavelets and a multiresolution analysis, which exploits the relationship between analysing filters and Floquet's solution of Mathieu differential equations. The transfer function of both the detail and…
Natural images are characterized by the multiscaling properties of their contrast gradient, in addition to their power spectrum. In this work we show that those properties uniquely define an {\em intrinsic wavelet} and present a suitable…
The influence of higher-order wavelet properties on the analytic wavelet transform behavior is investigated, and wavelet functions offering advantageous performance are identified. This is accomplished through detailed investigation of the…
We describe a generalized formalism, addressing the fundamental problem of reflection and transmission of complex optical waves at a plane dielectric interface. Our formalism involves the application of generalized operator matrices to the…