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• • • • 瑞利噪聲

瑞利噪聲

瑞利噪聲的PDF為
$$P(z)=\{\begin{array}{ll}\frac{2}{b}(z?a)e^{?(z?a{)}^2/b},& z\ge a\\ 0,& z<a\end{array}\text{\hspace{1em}(5.4)}$$

均值和方差為
$$\bar{z}=a+\sqrt{\pi b/4}\text{\hspace{1em}(5.5)}$$
$${\sigma }^2=\frac{b(4?\pi )}{4}\text{\hspace{1em}(5.6)}$$

def rayleigh_pdf(z, a=3, b=2):assert b != 0, "b is denominator, cannot be zero!!!"output = (2 / b )* (z - a) * np.exp(-((z - a)**2 )/b)output = np.where(z > a, output, 0)return output

更正下面代碼，如果之前已經復制的，也請更正

def add_rayleigh_noise(img, a=3):"""add rayleigh noise for imageparam: img: input image, dtype=uint8param: mean: noise meanparam: sigma: noise sigmareturn: image_out: image with rayleigh noise"""# image = np.array(img/255, dtype=float) # 這是有錯誤的，將得不到正確的結果，修改如下image = np.array(img, dtype=float)# ============== numpy.random.rayleigh======noise = np.random.rayleigh(a, size=image.shape)image_out = image + noiseimage_out = np.uint8(normalize(image_out)*255)return image_out # 瑞利PDF a = 10 b = 400 z = np.linspace(0, 255, 200)z_ = a + np.sqrt(np.pi*b/4) sigma = (b * (4 - np.pi)) / 4 peak_x = a + np.sqrt(b/2) peak_y = 0.607 * np.sqrt(2/b)print(f"z_ -> {z_}, sigma^2 -> {sigma}")rayleigh = rayleigh_pdf(z, a=a, b=b)plt.figure(figsize=(9, 6)) plt.plot(z, rayleigh), #plt.xticks([a, peak_x]), plt.yticks([0, peak_y]) plt.show() z_ -> 27.72453850905516, sigma^2 -> 85.84073464102069

# 瑞利噪聲 img_ori = cv2.imread("DIP_Figures/DIP3E_Original_Images_CH05/Fig0503 (original_pattern).tif", 0) # img_ori = np.ones((512, 512)) * 128 img_rayleigh = add_rayleigh_noise(img_ori, a=30)plt.figure(figsize=(9, 6)) plt.subplot(121), plt.imshow(img_ori, 'gray', vmin=0, vmax=255), plt.xticks([]), plt.yticks([]) plt.subplot(122), plt.imshow(img_rayleigh, 'gray', vmin=0, vmax=255), plt.xticks([]), plt.yticks([])plt.tight_layout() plt.show()

hist, bins = np.histogram(img_rayleigh.flatten(), bins=255, range=[0, 255], density=True) bar = plt.bar(bins[:-2], hist[:-1])

總結

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