12 citations · 16 across the 12 of their papers we have counts for
13 papers
On Random Fields Associated with Analytic Wavelet Transform
Gi-Ren Liu, Yuan-Chung Sheu, Hau-Tieng Wu
Despite the broad application of the analytic wavelet transform (AWT), a systematic statistical characterization of its magnitude and phase as inhomogeneous random fields on the ti…
Probabilistic Analysis of Scalogram Ridges in Signal Processing
Gi-Ren Liu, Yuan-Chung Sheu, Hau-Tieng Wu
While ridges in the scalogram, determined by the squared modulus of analytic wavelet transform (AWT), is a widely accepted concept and utilized in nonstationary time series analysi…
Ridge detection for nonstationary multicomponent signals with time-varying wave-shape functions and its applications
Yan-Wei Su, Gi-Ren Liu, Yuan-Chung Sheu +1
We introduce a novel ridge detection algorithm for time-frequency (TF) analysis, particularly tailored for intricate nonstationary time series encompassing multiple non-sinusoidal…
Gaussian Approximation for the Moving Averaged Modulus Wavelet Transform and its Variants
Gi-Ren Liu, Yuan-Chung Sheu, Hau-Tieng Wu
The moving average of the complex modulus of the analytic wavelet transform provides a robust time-scale representation for signals to small time shifts and deformation. In this wo…
When Scattering Transform Meets Non-Gaussian Random Processes, a Double Scaling Limit Result
Gi-Ren Liu, Yuan-Chung Sheu, Hau-Tieng Wu
We explore the finite dimensional distributions of the second-order scattering transform of a class of non-Gaussian processes when all the scaling parameters go to infinity simulta…
Asymptotic Analysis of Higher-order Scattering Transform of Gaussian Processes
Gi-Ren Liu, Yuan-Chung Sheu, Hau-Tieng Wu
We analyze the scattering transform with the quadratic nonlinearity (STQN) of Gaussian processes without depth limitation. STQN is a nonlinear transform that involves a sequential…
Central and Non-central Limit Theorems arising from the Scattering Transform and its Neural Activation Generalization
Gi-Ren Liu, Yuan-Chung Sheu, Hau-Tieng Wu
Motivated by analyzing complicated and non-stationary time series, we study a generalization of the scattering transform (ST) that includes broad neural activation functions, which…
Explore intrinsic geometry of sleep dynamics and predict sleep stage by unsupervised learning techniques
Gi-Ren Liu, Yu-Lun Lo, Yuan-Chung Sheu +1
We propose a novel unsupervised approach for sleep dynamics exploration and automatic annotation by combining modern harmonic analysis tools. Specifically, we apply diffusion-based…
Diffuse to fuse EEG spectra -- intrinsic geometry of sleep dynamics for classification
Gi-Ren Liu, Yu-Lun Lo, John Malik +2
We propose a novel algorithm for sleep dynamics visualization and automatic annotation by applying diffusion geometry based sensor fusion algorithm to fuse spectral information fro…
Phase Retrieval by Linear Algebra
P. Chen, A. Fannjiang, G. Liu
The null vector method, based on a simple linear algebraic concept, is proposed as a solution to the phase retrieval problem. In the case with complex Gaussian random measurement m…
Phase Retrieval with One or Two Diffraction Patterns by Alternating Projection with Null Initialization
Pengwen Chen, Albert Fannjiang, Gi-Ren Liu
Alternating projection (AP) of various forms, including the Parallel AP (PAP), Real-constrained AP (RAP) and the Serial AP (SAP), are proposed to solve phase retrieval with at most…
Multi-scaling Limits for Relativistic Diffusion Equations with Random Initial Data
Gi-Ren Liu, Narn-Rueih Shieh
Let be the spatial-temporal random field arising from the solution of a relativistic diffusion equation with the spatial-fra…
Homogenization of Fractional Kinetic Systems with Random Initial Data
Gi-Ren Liu, Narn-Rueih Shieh
Let be the -valued spatial-temporal random field arising from a certain two-equation system…