编写基于完全约束最小二乘法(Fully Constrained Least Squares,FCLS)的遥感影像光谱解混的python代码实现，读取tif数据使用gdal,数据分析使用numpy

在Python中，我们可以结合GDAL读取TIFF文件，NumPy进行数值计算，以及基于完全约束最小二乘法（FCLS）进行遥感影像光谱解混。这里给出一个简化版的实现，假设你已经有了每个传感器的校准系数矩阵和目标地物的光谱曲线：

from osgeo import gdal
import numpy as np
import scipy.optimize as optimize

# 读取TIFF文件
def read_tiff(file_path):
    dataset = gdal.Open(file_path)
    data = dataset.ReadAsArray()
    return data

# 完全约束最小二乘解混
def fcls_deconvolution(band_data, calibration_matrices, reference_spectra):
    def residual(c):
        return np.sum((np.dot(calibration_matrices, c) - band_data) ** 2)

    initial_guess = np.ones((reference_spectra.shape[0], 1))
    bounds = [(0, None)] * initial_guess.shape[0]  # 确保所有成分非负
    result = optimize.minimize(residual, initial_guess, method='SLSQP', bounds=bounds)
    deconvolved_spectrum = result.x

    return deconvolved_spectrum

# 示例用法
file_path = 'path_to_your_image.tif'
band_data = read_tiff(file_path)
calibration_matrices = ...  # 校准系数矩阵
reference_spectra = ...  # 目标地物参考光谱

deconvolved_spectrum = fcls_deconvolution(band_data, calibration_matrices, reference_spectra)
print("解混后的光谱:", deconvolved_spectrum)