Regularization for uniform spatial resolution properties in penalized-likelihood image reconstruction

Traditional space-invariant regularization methods in tomographic image reconstruction using penalized-likelihood estimators produce images with nonuniform spatial resolution properties. The local point spread functions that quantify the smoothing properties of such estimators are space variant, asymmetric, and object-dependent even for space invariant imaging systems. The authors propose a new quadratic regularization scheme for tomographic imaging systems that yields increased spatial uniformity and is motivated by the least-squares fitting of a parameterized local impulse response to a desired global response. The authors have developed computationally efficient methods for PET systems with shift-invariant geometric responses. They demonstrate the increased spatial uniformity of this new method versus conventional quadratic regularization schemes in simulated PET thorax scans.