1D synchrosqueezed wave packet transforms (SSWPT): Analyzing instantaneous properties (instantaneous frequencies, phases and amplitudes) of non-linear oscillatory signals in a superposition. 2D synchrosqueezed curvelet transform (SSCT): Anlayzing local properties of non-linear oscillatory textures in a superposition.
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README.md
SetPath.m

README.md

SynLab

  1. OVERVIEW

1D synchrosqueezed wave packet transforms (SSWPT):
Analyzing instantaneous properties (instantaneous frequencies, phases and amplitudes) of non-linear oscillatory signals in a superposition.

2D synchrosqueezed curvelet transform (SSCT):
Anlayzing local properties of non-linear oscillatory textures in a superposition.

3D synchrosqueezed wave packet transforms (SSWPT):

Applications:

Geophysics: seismic wave field separation and ground-roll removal.

Materials science: atomic crystal image analysis, grain boundary and local defects identification, elastic deformation estimation.

Art: Canvas painting analysis for art forensics.

  1. INTRODUCTION

SynLab is a collection of Matlab and MEX routines which implements 1D and 2D synchrosqueezed transforms proposed in [1]-[4]. It contains numerical examples in [2][5][6][9].

[1] H. Yang. Synchrosqueezed wave packet transforms and diffeomorphism based spectral analysis for 1d general mode decompositions. Applied and Computational Harmonic Analysis, 39(1):33 – 66, 2015.

[2] H. Yang, J. Lu, and L. Ying. Crystal image analysis using 2D synchrosqueezed transforms. Multiscale Modeling & Simulation, 13(4):1542–1572, 2015.

[3] H. Yang and L. Ying. Synchrosqueezed wave packet transform for 2d mode decompo- sition. SIAM Journal on Imaging Sciences, 6(4):1979–2009, 2013.

[4] H. Yang and L. Ying. Synchrosqueezed curvelet transform for two-dimensional mode decomposition. SIAM Journal on Mathematical Analysis, 46(3):2052–2083, 2014.

[5] H. Yang. Statistical analysis of synchrosqueezed transforms, Applied and Computational Harmonic Analysis, 2017.

[6] H. Yang, J. Lu, W. P. Brown, I. Daubechies, and L. Ying, Quantitative Canvas Weave Analysis Using 2D Synchrosqueezed Transforms. IEEE Signal Processing Magazine, Special Issue on Art Investigations, 2015.

[7] J. Lu, B. Wirth and H. Yang. Compbining 2d synchrosqueezed wave packet transforms with optimization for crystal image analysis. Journal of the Mechanics and Physics of Solids, pp. –, 2016. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0022509616300023

[8] H. Yang. Oscillatory data analysis and fast algorithms for integral operators, Ph.D. thesis, Stanford University, 2015.

[9] Bruno Cornelis, Haizhao Yang, Alex Goodfriend, Noelle Ocon, Jianfeng Lu, and Ingrid Daubechies, Removal of Canvas Patterns in Digital Acquisitions of Paintings, IEEE Transactions on Image Processing, Volume: 26, Issue: 1, Jan. 2017.

  1. INSTALLING SYNLAB

run the file SetPath.m first. It will automatically add all the MATLAB codes to your MATLAB path and compile all MEX files. After this, you can run all demo codes to see how to use this tool box.

  1. COPY RIGHT

SynLab is copyright reserved. For further information, please contact Haizhao Yang at haizhao@math.duke.edu Jianfeng Lu at jianfeng@math.duke.edu Lexing Ying at lexing@math.stanford.edu