Uniform Quadratic Penalties Cause Nonuniform Spatial Resolution

Abstract

Examines the spatial resolution properties of penalized maximum-likelihood image reconstruction methods by analyzing the local impulse response. The authors show that for emission image reconstruction using the ordinary uniform quadratic regularization penalty, the local impulse response is spatially variant. Paradoxically, the local resolution is poorest in high activity regions. The analysis leads naturally to a modified quadratic regularization penalty that achieves nearly uniform resolution. The modified penalty also provides a very practical method for choosing the smoothing parameter to obtain a specified resolution.