Image Denoising Method Using Wavelet-Domain Hidden Markov Tree Models with Code Implementation

In this article, we provide a detailed introduction to the implementation code for image denoising using wavelet-domain Hidden Markov Tree (HMT) models. First, let's understand the fundamentals of wavelet-based image denoising. This technique leverages signal processing principles by decomposing images into different frequency components and applying denoising procedures to each component individually, resulting in effective noise reduction. The implementation typically involves using wavelet transform functions (e.g., wavedec2 in MATLAB) to obtain approximation and detail coefficients at multiple resolution levels.

Next, we explore the application of Hidden Markov Tree models in image denoising. HMT is a probabilistic framework that models dynamic systems with hidden states. In image processing, we treat the image as a dynamic system where each pixel possesses hidden states representing clean and noisy characteristics. By constructing HMT models through expectation-maximization algorithms, we can achieve more accurate statistical modeling of wavelet coefficients. Key implementation aspects include training HMT parameters using the EM algorithm and designing state transition probabilities that capture parent-child relationships in wavelet coefficient trees.

Finally, we present the complete implementation code for HMT-based image denoising. The code structure typically includes: wavelet decomposition, HMT parameter estimation, coefficient thresholding based on posterior probabilities, and wavelet reconstruction. Critical functions involve hmt_train for model training and hmt_denoise for applying the denoising algorithm. Using this implementation, researchers can easily integrate HMT denoising into their projects, achieving superior performance compared to conventional methods. The code provides configurable parameters for wavelet types, decomposition levels, and noise estimation methods to accommodate different application scenarios.

This technical guide aims to assist researchers and engineers in implementing advanced wavelet-HMT denoising techniques effectively. The accompanying code documentation includes practical examples demonstrating performance comparison with standard denoising approaches.