做货代在哪个网站找客源,工体商城网站建设,网站开发 图片服务器,腾讯云如何建设网站标题最小均方误差#xff08;维纳#xff09;滤波最小均方误差#xff08;维纳#xff09;滤波
目标是求未污染图像fff的一个估计f^\hat{f}f^#xff0c;使它们之间的均方误差最小。 e2E{(f−f^)2}(5.80)e^2 E \big\{(f - \hat{f})^2 \big\} \tag{5.80}e2E{(f−f^)2…
标题最小均方误差维纳滤波最小均方误差维纳滤波
目标是求未污染图像fff的一个估计f^\hat{f}f^使它们之间的均方误差最小。 e2E{(f−f^)2}(5.80)e^2 E \big\{(f - \hat{f})^2 \big\} \tag{5.80}e2E{(f−f^)2}(5.80)
误差函数的最小值在频率域中的表达比如下 F^(u,v)[H∗(u,v)Sf(u,v)Sf(u,v)∣H(u,v)∣2Sη(u,v)]G(u,v)[H∗(u,v)∣H(u,v)∣2Sη(u,v)/Sf(u,v)]G(u,v)[1H(u,v)∣H(u,v)∣2∣H(u,v)2K]G(u,v)(5.81)\begin{aligned} \hat{F}(u, v) \Bigg[\frac{H^*(u, v) S_{f}(u, v)}{S_{f}(u, v)|H(u, v)|^2 S_{\eta}(u, v)} \Bigg] G(u, v) \\ \Bigg[\frac{H^*(u, v) }{|H(u, v)|^2 S_{\eta}(u, v) / S_{f}(u, v)} \Bigg] G(u, v) \\ \Bigg[\frac{1}{H(u,v)} \frac{|H(u,v)|^2}{|H(u,v)^2 K} \Bigg]G(u,v) \end{aligned} \tag{5.81}F^(u,v)[Sf(u,v)∣H(u,v)∣2Sη(u,v)H∗(u,v)Sf(u,v)]G(u,v)[∣H(u,v)∣2Sη(u,v)/Sf(u,v)H∗(u,v)]G(u,v)[H(u,v)1∣H(u,v)2K∣H(u,v)∣2]G(u,v)(5.81)
注逆滤波与维纳滤波都要求未退化图像和噪声的功率谱是已知的。
# 运动模糊PSF与谱
fft_shift np.fft.fftshift(PSF)
fft np.fft.fft2(PSF)
spect spectrum_fft(fft)
plt.figure(figsize(8, 8))
plt.subplot(1,2,1), plt.imshow(PSF, gray)
plt.subplot(1,2,2), plt.imshow(spect, gray)
plt.show()# 仿真运动模糊
def motion_process(image_size, motion_angle, degree15):This function has some problemPSF np.zeros(image_size)
# print(image_size)center_position(image_size[0]-1)/2
# print(center_position)slope_tanmath.tan(motion_angle*math.pi/180)slope_cot1/slope_tanif slope_tan1:for i in range(degree):offsetround(i*slope_tan) #((center_position-i)*slope_tan)PSF[int(center_positionoffset),int(center_position-offset)]1return PSF / PSF.sum() #对点扩散函数进行归一化亮度else:for i in range(degree):offsetround(i*slope_cot)PSF[int(center_position-offset),int(center_positionoffset)]1return PSF / PSF.sum()def get_motion_dsf(image_size, motion_angle, motion_dis):Get motion PSFparam: image_size: input image shapeparam: motion_angle: blur motion angleparam: motion_dis: blur distant, the greater value, more blurredreturn normalize PSFPSF np.zeros(image_size) # 点扩散函数x_center (image_size[0] - 1) / 2y_center (image_size[1] - 1) / 2sin_val np.sin(motion_angle * np.pi / 180)cos_val np.cos(motion_angle * np.pi / 180)# 将对应角度上motion_dis个点置成1for i in range(motion_dis):x_offset round(sin_val * i)y_offset round(cos_val * i)PSF[int(x_center - x_offset), int(y_center y_offset)] 1return PSF / PSF.sum() # 归一化# 对图片进行运动模糊
def make_blurred(input, PSF, eps):blurred image with PSFparam: input: input imageparam: PSF: input PSF maskparam: eps: epsilon, very small value, to make sure not divided or multiplied by zeroreturn blurred imageinput_fft np.fft.fft2(input) # image FFTPSF_fft np.fft.fft2(PSF) eps # PSF FFT plus epsilonblurred np.fft.ifft2(input_fft * PSF_fft) # image FFT multiply PSF FFTblurred np.abs(np.fft.fftshift(blurred))return blurreddef inverse_filter(input, PSF, eps): inverse filter using FFT to denoiseparam: input: input imageparam: PSF: known PSFparam: eps: epsiloninput_fft np.fft.fft2(input)PSF_fft np.fft.fft2(PSF) eps #噪声功率这是已知的考虑epsilonresult np.fft.ifft2(input_fft / PSF_fft) #计算F(u,v)的傅里叶反变换result np.abs(np.fft.fftshift(result))return resultdef wiener_filter(input, PSF, eps, K0.01):wiener filter for image denoiseparam: input: input imageparam: PSF: input the PSF maskparam: eps: epsilonparam: K0.01: K value for wiener fuctionreturn image after wiener filterinput_fft np.fft.fft2(input)PSF_fft np.fft.fft2(PSF) epsPSF_fft_1 np.conj(PSF_fft) / (np.abs(PSF_fft)**2 K)# 按公式居然得不到正确的值
# PSF_abs PSF * np.conj(PSF)
# PSF_fft_1 (1 / (PSF eps)) * (PSF_abs / (PSF_abs K))result np.fft.ifft2(input_fft * PSF_fft_1)result np.abs(np.fft.fftshift(result))return result# 要实现的功能都在这里调用
if __name__ __main__:image cv2.imread(DIP_Figures/DIP3E_Original_Images_CH05/Fig0526(a)(original_DIP).tif, 0)# 显示原图像plt.figure(1, figsize(6, 6))plt.title(Original Image), plt.imshow(image, gray)plt.xticks([]), plt.yticks([])plt.figure(2, figsize(18, 12))# 进行运动模糊处理PSF get_motion_dsf(image.shape[:2], -50, 100)blurred make_blurred(image, PSF, 1e-3)plt.subplot(231), plt.imshow(blurred, gray), plt.title(Motion blurred)plt.xticks([]), plt.yticks([])# 逆滤波result inverse_filter(blurred, PSF, 1e-3) plt.subplot(232), plt.imshow(result, gray), plt.title(inverse deblurred)plt.xticks([]), plt.yticks([])# 维纳滤波result wiener_filter(blurred, PSF, 1e-3) plt.subplot(233), plt.imshow(result, gray), plt.title(wiener deblurred(k0.01))plt.xticks([]), plt.yticks([])# 添加噪声,standard_normal产生随机的函数blurred_noisy blurred 0.1 * blurred.std() * np.random.standard_normal(blurred.shape) # 显示添加噪声且运动模糊的图像plt.subplot(234), plt.imshow(blurred_noisy, gray), plt.title(motion noisy blurred)plt.xticks([]), plt.yticks([])# 对添加噪声的图像进行逆滤波result inverse_filter(blurred_noisy, PSF, 0.1 1e-3) plt.subplot(235), plt.imshow(result, gray), plt.title(inverse deblurred)plt.xticks([]), plt.yticks([])# 对添加噪声的图像进行维纳滤波result wiener_filter(blurred_noisy, PSF, 0.1 1e-3) plt.subplot(236), plt.imshow(result, gray), plt.title(wiener deblurred(k0.01))plt.xticks([]), plt.yticks([])plt.tight_layout()plt.show()# 要实现的功能都在这里调用
if __name__ __main__:image cv2.imread(DIP_Figures/DIP3E_Original_Images_CH05/Fig0526(a)(original_DIP).tif, 0)# 显示原图像plt.figure(1, figsize(6, 6))plt.title(Original Image), plt.imshow(image, gray)plt.xticks([]), plt.yticks([])plt.figure(2, figsize(18, 12))# 进行运动模糊处理PSF get_motion_dsf(image.shape[:2], -45, 95)blurred cv2.imread(DIP_Figures/DIP3E_Original_Images_CH05/Fig0529(d)(medium_noise_var_pt01).tif, 0)plt.subplot(231), plt.imshow(blurred, gray), plt.title(Motion blurred)plt.xticks([]), plt.yticks([])# 逆滤波result inverse_filter(blurred, PSF, 1e-3) plt.subplot(232), plt.imshow(result, gray), plt.title(inverse deblurred)plt.xticks([]), plt.yticks([])# 维纳滤波result wiener_filter(blurred, PSF, 1e-3, K0.01) plt.subplot(233), plt.imshow(result, gray), plt.title(wiener deblurred(k0.01))plt.xticks([]), plt.yticks([])# 添加噪声,standard_normal产生随机的函数blurred_noisy blurred 0.1 * blurred.std() * np.random.standard_normal(blurred.shape) # 显示添加噪声且运动模糊的图像plt.subplot(234), plt.imshow(blurred_noisy, gray), plt.title(motion noisy blurred)plt.xticks([]), plt.yticks([])# 对添加噪声的图像进行逆滤波result inverse_filter(blurred_noisy, PSF, 0.1 1e-3) plt.subplot(235), plt.imshow(result, gray), plt.title(inverse deblurred)plt.xticks([]), plt.yticks([])# 对添加噪声的图像进行维纳滤波result wiener_filter(blurred_noisy, PSF, 0.1 1e-3) plt.subplot(236), plt.imshow(result, gray), plt.title(wiener deblurred(k0.01))plt.xticks([]), plt.yticks([])plt.tight_layout()plt.show()
