Signal and Image Processing with Belief Propagation
Erik B. Sudderth, William T. Freeman · 2008
Many practical signal processing applications involve large, complex collections of hidden variables and uncertain parameters. For example, modern communication systems typically couple sophisticated error correcting codes with schemes for adaptive channel equalization. Additionally, many computer vision algorithms use prior knowledge about the statistics of typical surfaces to infer the three–dimensional (3D) shape of a scene from ambiguous, local image measurements. Probabilistic graphical models provide a powerful, general framework for designing systems like these. In this approach, graphs are used to decompose joint distributions into a set of local constraints and dependencies. Such modular structure provides an intuitive language for expressing domain–specific knowledge, and facilitates transfer of modeling advances to new applications. Once a problem has been formulated using a graphical model, a wide range of efficient algorithms for statistical learning and inference can then be directly applied. In this column, we review a particularly effective inference algorithm known as belief propagation (BP). After describing its message–passing structure, we demonstrate the interplay of statistical modeling and inference in two challenging applications: denoising discrete signals