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This thesis is based on the technology of Compressed Sensing and the study of the algorithms of Approximate Message Passing for the single-pixel camera. This thesis has been developed in the institute of telecommunication in the Technische Universität Wien (TU Wien) led by the research group of the professor Norbert Görtz. In the beginning of the thesis it is explained what a single-pixel camera is and it also talks about what compressed sensing is, later on, two necessarily iterative schemes (Iterative Hard Thresgolding i Iterative Soft Thresholding) are defined to understand the algorithms of Approximate Message Passing (AMP) and its Bayesian derivation (Bayesian Approximate Message Passing, BAMP). The theoretical explanation of the operation of these algorithms is implicit in the thesis, moreover, AMP and BAMP are implemented in Matlab coding. This implementation allows to see the behaviour of these algorithms in different scenarios to fully understand the differences between them.