Recently, an elegant method based on the wavelet decomposition has been developed for the recovery of a thick specimen's depth profile in microscopy. A stack of images of the object at different focal distances is acquired, showing different parts of the object in focus each time. The wavelet transform allows to identify the in-focus regions of each image and combine them into one single sharp image, said with extended depth-of-field (EDF). The aim of this project is to study the feasibility of using hidden markov models (HMM) in the wavelet domain for this application. We expect the HMM to replace the current "consistency checks" in a more general way. Additionally, the hidden state of the wavelet coefficients can represent the out-of-focus distance and the corresponding estimated probability density function could be seen under the effect of the point spread function of the microscope. After an introduction on wavelets, the current EDF approach, and HMM applied to wavelets, the project consists of developing a Matlab prototype. The implementation of HMM needs an expectation-maximisation (EM) algorithm, for which already Matlab examples are available on the Internet. Once the various parameters and settings of the algorithm are well understood, an implementation in Java as a plug-in for ImageJ will be considered. This project is in collaboration with Prof. Brigitte Forster, TUM, Munich, Germany.