Doğrusal sistemlerde yapısal ve ölçevsel bilgi

We present a systematic approach to understand the information-theoretic re-lationships in linear systems. Our main aim is to understand what kind ofinformation the output of a linear system carries about the input of the systemand how much of this information is preserved in the measurement process. Werecognize structural and metrical information as two fundamental concepts forclassifying the information content of signals. We base our understanding of theproblem on information-theoretic concepts like entropy, mutual information andchannel capacity. We present our results as trade-offs between cost and perfor-mance, yielding insights about different aspects of the information flow in a linearsystem. We especially focus on building a framework which indicates how accu-rately, and how many measurements must be made and how the measurementlocations should be selected.Keywords: inverse problems, signal recovery, structural information, metricalinformation, experiment design, measurement problem, information theory, frac-tional Fourier transform, wave propagation, optical information processingiii