Wavelet Domain Hmm Model In Image Processing Applications

Wavelet-based statistical signal processing techniques such as denoising and detection typically model the wavelet coefficients as independent or jointly Gaussian. These models are unrealistic for many real world signals. Hidden Markov models(HMMs), a type of finite state machines for statistical modeling, have been successfully applied to speech recognition due to the fact that finite states in speech signals are amenable to the mechanism of HMMs. However, it is hard to directly apply HMMs to image modeling in the spatial domain, since there are too many states(gray-levels of pixels) in real-world images. In this paper, we introduce a new framework for statistical signal processing based on wavelet-domain hidden Markov models (HMMs) that concisely models the statistical dependencies and nonGaussian statistics encountered in real-world signals, since the wavelet transform can decorrelate image data by reducing the number of states of wavelet coefficients, thus making wavelet-domain HMMs manipulable and useful for statistical image modeling. Efficient Expetation Maxmization algorithms are developed for fitting the HMMs to observational signal data. The new framework is suitable for a wide range of applications, including signal estimation, detection, classification, predication, and even synthesis.In this paper, we apply this model on image processing, including image denoising and texture analysis, for image denoising, we develop a novel algorithms for image denoising. We combine the Expectation Maximization algorithms with the traditional denoising algorithm, that we get the state-of-the-art image denoising performance, for texture analysis, a new wavelet-domain HMM, HMT-3S, is developed for more accurate statistical texture characterization, and the maximum likelihood(ML) based texture classification is developed. It is shown the HMT-3S can attain the excellent results on both classification and segmentation..