基于多元高斯混合模型的图像去噪算法

Image Denoising Algorithm Based on Multivariate Gaussian Mixture Model

摘要: 高光谱图像(Hyperspectral Images, HSIs)在遥感和医学成像等领域具有广泛的应用，但在采集过程中容易受到各种噪声的干扰。尽管目前已有多种去噪方法应用于高光谱图像处理，但这些方法在应对复杂光谱特征和复杂或非均匀噪声分布时仍面临挑战，且部分方法可能导致图像细节的丢失，降低光谱数据的真实性和有效性。为克服这些不足，文章提出了一种基于多元高斯混合模型的高光谱图像去噪方法。该方法将噪声建模为多元高斯混合模型，通过多模态特征表示图像的复杂光谱结构，以更好地适应不同光谱分布。我们采用变分贝叶斯(Variational Bayes, VB)方法进行参数估计，从而改善了传统期望最大化(EM)算法易于陷入局部最优的局限性，提高了参数估计的稳定性和模型收敛效率。实验结果表明，本文方法在多个数据集和多种噪声情况下均表现出优异的去噪效果，还能更好地保持光谱特性和图像结构的一致性，验证了其在高光谱图像去噪任务中的有效性。

Abstract: Hyperspectral Images (HSIs) have widespread applications in fields such as remote sensing and medical imaging, but they are often subject to various types of noise during the acquisition process. Despite the availability of numerous denoising methods for HSI processing, these methods still face challenges in handling complex spectral features and non-uniform noise distributions, which may lead to the loss of image details and compromise the authenticity and effectiveness of spectral data. To address these shortcomings, this paper proposes a hyperspectral image denoising method based on a multivariate Gaussian mixture model. The proposed method models noise using a multivariate Gaussian mixture model, employing multimodal features to represent the complex spectral structure of images, thereby better adapting to diverse spectral distributions. We adopt the Variational Bayes (VB) method for parameter estimation to overcome the limitations of the traditional Expectation-Maximization (EM) algorithm, which tends to get stuck in local optima, thus improving the stability of parameter estimation and convergence efficiency. Experimental results demonstrate that the proposed method achieves superior denoising performance across multiple datasets and various noise levels, while also better preserving spectral characteristics and image structure, validating its effectiveness for HSI denoising tasks.