使用Directional Lifting Wavelet Transform处理RGB图像的python代码及其逆变换

以下是使用Directional Lifting Wavelet Transform处理RGB图像的Python代码及其逆变换：

import numpy as np
from scipy import signal

def forward_transform_2d(image):
    """
    Performs a 2D directional lifting wavelet transform on an image.
    
    Parameters:
        image (ndarray): Input image to transform.
    
    Returns:
        (ll, lh, hl, hh) (tuple of ndarrays): Tuple of subbands obtained from the transform.
    """
    # Define filters
    h0 = np.array([1, 2, 1])/4
    g0 = np.array([-1, 2, -1])/4
    h1 = np.array([1, -2, 1])/4
    g1 = np.array([1, 2, 1])/4
    
    # Split into RGB channels
    r = image[:,:,0]
    g = image[:,:,1]
    b = image[:,:,2]
    
    # Apply filters to each channel
    llr = signal.convolve2d(r, h0[np.newaxis, :], mode='same', boundary='symm')
    lhr = signal.convolve2d(r, g0[np.newaxis, :], mode='same', boundary='symm')
    hlr = signal.convolve2d(r, h1[np.newaxis, :], mode='same', boundary='symm')
    hhr = signal.convolve2d(r, g1[np.newaxis, :], mode='same', boundary='symm')
    
    llg = signal.convolve2d(g, h0[np.newaxis, :], mode='same', boundary='symm')
    lhg = signal.convolve2d(g, g0[np.newaxis, :], mode='same', boundary='symm')
    hlg = signal.convolve2d(g, h1[np.newaxis, :], mode='same', boundary='symm')
    hhg = signal.convolve2d(g, g1[np.newaxis, :], mode='same', boundary='symm')
    
    llb = signal.convolve2d(b, h0[np.newaxis, :], mode='same', boundary='symm')
    lhb = signal.convolve2d(b, g0[np.newaxis, :], mode='same', boundary='symm')
    hlb = signal.convolve2d(b, h1[np.newaxis, :], mode='same', boundary='symm')
    hhb = signal.convolve2d(b, g1[np.newaxis, :], mode='same', boundary='symm')
    
    # Combine subbands into tuples
    ll = (llr, llg, llb)
    lh = (lhr, lhg, lhb)
    hl = (hlr, hlg, hlb)
    hh = (hhr, hhg, hhb)
    
    return ll, lh, hl, hh
    
def inverse_transform_2d(ll, lh, hl, hh):
    """
    Performs a 2D directional lifting wavelet inverse transform on subbands.
    
    Parameters:
        ll (ndarray): Low-low subband of the transform.
        lh (ndarray): Low-high subband of the transform.
        hl (ndarray): High-low subband of the transform.
        hh (ndarray): High-high subband of the transform.
    
    Returns:
        output (ndarray): Reconstructed image obtained from the inverse transform.
    """
    # Define filters
    h0 = np.array([1, 2, 1])/4
    g0 = np.array([-1, 2, -1])/4
    h1 = np.array([1, -2, 1])/4
    g1 = np.array([1, 2, 1])/4
    
    # Combine RGB subbands
    r = ll[0] + lh[0] + hl[0] + hh[0]
    g = ll[1] + lh[1] + hl[1] + hh[1]
    b = ll[2] + lh[2] + hl[2] + hh[2]
    
    # Define inverse filters
    h0_inv = -g0
    g0_inv = h0
    h1_inv = -g1
    g1_inv = h1
    
    # Perform inverse transform on each channel
    for i in range(3):
        # Upsample
        r_up = signal.upfirdn(h0_inv, r[:,i], 2, axis=0)
        lhr_up = signal.upfirdn(g0_inv, lh[i][:,1:], 2, axis=0) # Omit boundary samples
        hlr_up = signal.upfirdn(h1_inv, hl[i][:,1:], 2, axis=0) # Omit boundary samples
        hhr_up = signal.upfirdn(g1_inv, hh[i][:,1:], 2, axis=0) # Omit boundary samples
        
        # Add
        r_up = r_up + lhr_up + hlr_up + hhr_up
        
        # Reapply original filters
        r_up = signal.convolve2d(r_up, h0[np.newaxis, :], mode='same', boundary='symm')
        g_up = signal.convolve2d(r_up, g0[np.newaxis, :], mode='same', boundary='symm')
        h_up = signal.convolve2d(r_up, h1[np.newaxis, :], mode='same', boundary='symm')
        hh_up = signal.convolve2d(r_up, g1[np.newaxis, :], mode='same', boundary='symm')
        
        # Combine subbands
        output = np.stack((r_up, g_up, h_up), axis=2)
    
    return output

注意：这里使用的是symmetric边界处理方式。这个函数只能处理size为2^n * 2^n的输入图像。