Image denoising using Improved Semantic Approximation Algorithm in wavelet domain Hidden Markov model

Wavelet-domain Hidden Markov models (HMMs) have been recently proposed and applied to image processing especially to image denoising. In the proposed algorithm called Improved Semantic Approximation Algorithm (ISAA), Hidden Markov Model is used in image filtering into which Gaussian Mixture field is introduced. In this process, the image coefficients are assumed to locally follow Gaussian mixture distributions determined by their neighbourhoods. Further, Hidden Markov Tree is used in ISAA to couple the mixture assignments at neighbouring nodes. The denoised image is then filtered by proposed HMMs. Image restoration is achieved by applying Local Polynomial Approximation-Intersection of Confidence Interval (LPA-ICI) rule for each pixel. Here, an Expectation-Maximization algorithm is adapted for image restoration with a higher contrast and to estimate the parameters required for LPA kernels. The quantitative measure for the clarity of the images is given by PSNR. An attempt is made for the first time to calculate PSNR value in log 2 scale and compared that with log 10 scale. Based on these values similarities between various tested images is carefully investigated.