我正在研究图像之间的比较以确定质量。我已经了解了 MSE、SNR 和 PSNR，现在我正在尝试了解 WSNR，我认为它类似于 SNR，但具有权重。

我有一个 Python 代码来计算两个图像之间的 WSNR，但我并不完全理解它，也不知道这个度量的数学定义是什么。我找不到任何解释它是如何定义和计算的论文或书籍。

问题：

WSNR（加权信噪比）是如何定义的？

蟒蛇代码：

import numpy as np
from scipy.ndimage.filters import gaussian_filter as __gaussian_filter
from scipy.ndimage.filters import convolve as __convolve
from scipy.ndimage.filters import correlate as __correlate
from scipy.fftpack import fftshift as __fftshift

def wsnr(reference, query):
"""Computes the Weighted Signal to Noise Ratio (WSNR) metric.

    value = wsnr(reference, query)

    inputs
    ----------
    reference: original image data.
    query    : modified image data to be compared.

    output
    ----------
    value    : wsnr value
    """
    def __genetate_meshgrid(x, y):
        f = lambda u: u / 2 + 0.5 - 1
        (H, W) = map(f, (x, y))
        return (H, W)

    def __create_complex_planes(x, y):
        (H, W) = __genetate_meshgrid(x, y)
        (xplane, yplane) = np.mgrid[-H:H + 1, -W:W + 1]
        return (xplane, yplane)

    def __get_evaluated_contrast_sensivity(plane):
        w = 0.7
        angle = np.angle(plane)
        return ((1.0 - w) / 2.0) * np.cos(4.0 * angle) + (1.0 + w) / 2.0

    def __get_radial_frequency(x, y):
        (xplane, yplane) = __create_complex_planes(x, y)
        nfreq = 60
        plane = (xplane + 1.0j * yplane) / x * 2.0 * nfreq
        s = __get_evaluated_contrast_sensivity(plane)
        radfreq = abs(plane) / s
        return radfreq

    def __generate_CSF(radfreq):
        a = -((0.114 * radfreq) ** 1.1)
        csf = 2.6 * (0.0192 + 0.114 * radfreq) * np.exp(a)
        f = radfreq < 7.8909
        csf[f] = 0.9809
        return csf

    def __weighted_fft_domain(ref, quer, csf):
        err = ref.astype('double') - quer.astype('double')
        err_wt = __fftshift(np.fft.fft2(err)) * csf
        im = np.fft.fft2(ref)
        return (err, err_wt, im)

    def __get_weighted_error_power(err_wt):
        return (err_wt * np.conj(err_wt)).sum()

    def __get_signal_power(im):
        return (im * np.conj(im)).sum()

    def __get_ratio(mss, mse):
        if mse != 0:
            ratio = 10.0 * np.log10(mss / mse)
        else:
            ratio = float("inf")
        return np.real(ratio)

    if not len(reference.shape) < 3:
        reference = __convert_to_luminance(reference)
        query = __convert_to_luminance(query)
    size = reference.shape
    (x, y) = (size[0], size[1])
    radfreq = __get_radial_frequency(x, y)
    csf = __generate_CSF(radfreq)
    (err, err_wt, im) = __weighted_fft_domain(reference, query, csf)
    mse = __get_weighted_error_power(err_wt)
    mss = __get_signal_power(im)
    ratio = __get_ratio(mss, mse)
    return ratio