Editing Iterative reconstruction (section)

=== Statistical reconstruction ===
There are typically five components to statistical iterative image reconstruction algorithms, e.g.<ref name="pwl">{{cite journal | author = Fessler J A | year = 1994 | title = Penalized weighted least-squares image reconstruction for positron emission tomography | url =https://deepblue.lib.umich.edu/bitstream/2027.42/85851/1/Fessler105.pdf | journal = IEEE Transactions on Medical Imaging | volume = 13 | issue = 2| pages = 290–300 | doi=10.1109/42.293921| pmid = 18218505 | hdl = 2027.42/85851 | hdl-access = free }}</ref>
# An object model that expresses the unknown continuous-space function <math>f(r)</math> that is to be reconstructed in terms of a finite series with unknown coefficients that must be estimated from the data.
# A system model that relates the unknown object to the "ideal" measurements that would be recorded in the absence of measurement noise.  Often this is a linear model of the form <math>\mathbf{A}x+\epsilon</math>, where <math>\epsilon</math> represents the noise.
# A [[statistical model]] that describes how the noisy measurements vary around their ideal values. Often [[Gaussian noise]] or [[Poisson statistics]] are assumed. Because [[Poisson statistics]] are closer to reality, it is more widely used.
# A [[Loss function|cost function]] that is to be minimized to estimate the image coefficient vector. Often this cost function includes some form of [[regularization (mathematics)|regularization]]. Sometimes the regularization is based on [[Markov random fields]].
# An [[algorithm]], usually iterative, for minimizing the cost function, including some initial estimate of the image and some stopping criterion for terminating the iterations.