| Summary: | 碩士 === 國立臺灣科技大學 === 資訊工程系 === 97 === Diffusion process from physics and belief propagation from probabilistic graphical models are among two of the most popular methods for distributed computation. In many cases, we need the computation distributed locally in small area so that some tough nonlinear or time-consuming computational problems can be solved as a whole. For instance, we can solve image restoration problem by distributed computation. In the system, a pixel is represented by a node and the noisy image can be restored to a clearer version by the computation involving (only) interactions between neighboring nodes/pixels. Considering the importance of distributed computation, we do not easily find comprehensive and all-in-one materials that discuss all the related topics. The thesis is therefore in three folds. First, we would like to give a friendly introduction to many of the distributed computation methods, including diffusion, random walk, energy minimization, max-product “belief propagation” and sum-product “belief propagation”. We will go through some basic facts including some equivalence statements. For instance, the max-product is equivalent to diffusion process and random walk under some assumptions because all of them try to find the most probable configuration given the evidence. Also, we emphasize a formulation via energy minimization where many of the algorithms such as hard constraint or soft constraint problems can be represented as special cases of the formulation. Finally, we empirically compare between those related algorithms when the assumptions to guarantee equivalence fail. Especially, some cases will be discussed, the structure containing loops, the potential functions not equal to Gaussian, etc. We will concentrate on the problem of image restoration in our comparison.
|
|---|
