复小波结构相似性工具箱
Toolbox for Complex Wavelet
Structural Similarity Index Measure (CW-SSIM)

• 本项目是应用以下信号分析方法实现的CW-SSIM算法

• A little toolbox for two kinds of implementations of CW-SSIM with

  • 复数可控金字塔
  • Complex Steerable Pyramid
  • 双树复小波变换
  • Dual Tree-Complex Wavelet Transform (DT-CWT)

• 为了方便进行比较，同时实现了UIQI/SSIM和MS-SSIM

• For better comparison, the toolbox also put UIQI/SSIM and MS-SSIM in the toolbox.

• 特别感谢Nick Kingsbury教授的工作以及dtcwt_matlab项目分享的Matlab代码

• Special Thanks for Prof. Nick Kingsbury and the code from dtcwt_matlab repository.

• 声明：受限于作者知识水平，本项目可能存在运算错误

• Notice: There may be some errors in project due to author's limited knowledge.

• 如发现计算问题，欢迎提交中文或英文的Issue

• Glad to receive Chinese/English Issue if anyone finds calculation problems.

项目特色（Highlights）

• 实现了任意维度数据的双树复小波变换（1维、2维、3维、N维）

• Apply Dual Tree Complex Wavelet Transform (DT-CWT) on data with any dimensions (1-D, 2-D, 3-D, n-D).

• 输入数据可以高于双树复小波变换的实际处理维度

• Input dimension can be higher than the DT-CWT processing dimension

• 基于dtcwt_matlab中wavegen.m小波生成代码，实现了小波的按需求精度生成

• According to wavegen.m from dtcwt_matlab，wavelet can generate as demand.

• 实现了小波数值的缓存和数值保存，方便快速调用

• Support caching and storing values of wavelets to speed up calculation.

• CPU运算仅使用了numpy/scipy/sympy

• Only use numpy/scipy/sympy to achieve CPU calculation.

• GPU加速支持cupy和torch/pytorch

• Support GPU acceleration with cupy and torch/pytorch

• 各部分模块化，方便导入，易于扩展

• All the module are independent with each other. Easy to import and extent.

使用方法（Usage)

• 更多用法可以参考experiment.py
• More usages can reference experiment.py.

import skimage.io
import torch

import ssimlibs.torch

ssim = ssimlibs.torch.CwSSIM(
    backend='DualTree',
    levels=4,
    level_alpha1=ssimlibs.torch.NearSymmetricT13T19Wavelet(),
    level_others=ssimlibs.torch.QShiftT14Wavelet())
if __name__ == '__main__':
    a = skimage.util.img_as_float64(skimage.io.imread('pictures/elephant.jpg'))
    b = skimage.util.noise.random_noise(a, mode='speckle')
    with torch.device(0):
        result = ssim(torch.tensor(a), torch.tensor(b))
    print(float(result))

特殊说明（Notes)

• 由于cupy和torch/pytorch在下列函数的支持方面存在问题，小波计算使用numpy
• All wavelets calculate with numpy due to the compatible issues with cupy and torch/pytorch functions.
  • cupy
    • cupy.roots 和 cupy.poly 多项式系数不支持伴随矩阵为任意矩阵的特征值求解
    • cupy.roots and cupy.poly functions do not support polynomial coefficients whose companion matrices are general 2d square arrays.
  • torch/pytorch
    • torch/pytorch中没有numpy.roots, numpy.poly, scipy.linalg.toeplitz的直接支持
    • torch/pytorch is lack of direct supports with numpy.roots, numpy.poly and scipy.linalg.toeplitz.