全变差正则化图像结构层纹理层分解代码

以下是一个简单的全变差正则化图像分解代码，它将图像分解为结构层和纹理层：

import numpy as np
from scipy.ndimage.filters import convolve

def tv_norm(img):
    # 计算全变差范数
    dx = np.diff(img, axis=1)
    dy = np.diff(img, axis=0)
    d_norm = np.sqrt(dx**2 + dy**2)
    return np.sum(d_norm)

def decompose_image(img, niters=100, lmbda=0.1):
    # 进行图像分解
    u = np.zeros_like(img)
    px = np.zeros_like(img)
    py = np.zeros_like(img)

    for i in range(niters):
        u_old = u

        # 更新结构层
        rx = np.roll(px, shift=-1, axis=1)
        ry = np.roll(py, shift=-1, axis=0)
        ux = np.diff(u, axis=1)
        uy = np.diff(u, axis=0)
        px_new = rx + ux
        py_new = ry + uy
        norm_new = np.maximum(1, np.sqrt(px_new**2 + py_new**2)/lmbda)
        px = px_new / norm_new
        py = py_new / norm_new
        bx = np.roll(px, shift=1, axis=1)
        by = np.roll(py, shift=1, axis=0)
        div = (px - bx) + (py - by)
        u = img + div

        # 更新纹理层
        diff = u - img
        diff_filt = convolve(diff, np.array([[-1, 1]]))
        u = img + diff_filt * lmbda / (1 + lmbda * tv_norm(diff_filt))

        # 判断算法是否收敛
        if np.sum((u - u_old)**2) < 1e-5:
            break

    return u, img - u

代码中使用全变差正则化对图像进行分解，其中 `niters` 为迭代次数，`lmbda` 为正则化参数。分解后的结构层为 `u`，纹理层为 `img - u`。