The Thin Plate as a Regularizer in Bayesian SPECT Reconstruction

The attractions of the maximum-likelihood (ML) method for SPECT reconstruction, namely accurate system and noise modelling, are tempered by its unstable nature. The variety of Bayesian MAP approaches proposed in recent years can both stabilize the reconstructions and lead to better bias and variance. Our own work [1] used a nonquadratic prior (the weak plate) that imposed piecewise smoothness on the first derivative of the solution to achieve results superior to those obtained using a nonquadratic prior (the weak membrane) that imposed piecewise smoothness of the zeroth derivative. By relaxing the requirement of imposing spatial discontinuities and using instead a quadratic (no discontinuities) smoothing prior, algorithms become easier to analyze, solutions easier to compute, and hyperparameter calculation becomes less of a problem. In this work, we investigated whether the advantages of weak plate relative to weak membrane are retained when non-piecewise quadratic versions - the thin..