LinearSystems-Theory-2011

LinearSystems-Theory-2011 - Linear Systems Theory Andres...

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Unformatted text preview: Linear Systems Theory Andres Kriete School of Biomedical Engineering, Science and Health Systems Drexel University 2011 Presentation contains slides translated and/or modified from presentations of B. Preim, MEVIS, J. Pawley / W.Block, Wisconsin and Mikael Jensson, Sweden Linear Systems why study them? Develop general analysis tools for all modalities Applicable beyond medical imaging Tools provide valuable insights for understanding and design Rational for further improvement of systems Build upon your knowledge of one-dimensional theory Communications: time frequency (1 dimension) Imaging: space spatial frequency We will work in two dimensions. Cells and Human body is three-dimensional. Extension of 2D theory to three dimensions is straightforward. Properties of linear systems Linearity Conditions Let f 1 (x,y) and f 2 (x,y) describe two objects we want to image. f 1 (x,y) can be any object and represent any characteristic of the object. (e.g. color, intensity, temperature, texture, X-ray absorption, etc.) Assume each is imaged by some imaging device (system). Let f 1 (x,y) g 1 (x,y) f 2 (x,y) g 2 (x,y) Lets scale each object and combine them to form a new object. a f 1 (x,y) + b f 2 (x,y) hat is the output? If the system is linear, output is a g 1 (x,y) + b g 2 (x,y) Linearity Example: Is this a linear system? x x Linearity Example: Is this a linear system? 9 3 16 4 9 + 16 = 25 5 3 + 4 5 Not linear. x x xample in medical imaging: Analog to digital converter Doubling the X-ray photons doubles those transmitted Doubling the nuclear medicine doubles source & reception energy...
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LinearSystems-Theory-2011 - Linear Systems Theory Andres...

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