Pattern recognition (psychology)

Invariant (physics)

Image resolution

Mathematics

Mathematical physics

Algorithm

Image (mathematics)

Image restoration

Mathematical optimization

Quadratic equation

Iterative reconstruction

Mathematical analysis

Artificial intelligence

Regularization (linguistics)

Geometry

Computer science

Impulse response

Image processing

IEEE Transactions on Image Processing

This paper examines the spatial resolution properties of penalized-likelihood image reconstruction methods by analyzing the local impulse response. The analysis shows that standard regularization penalties induce space-variant local impulse response functions, even for space-invariant tomographic systems. Paradoxically, for emission image reconstruction, the local resolution is generally poorest in high-count regions. We show that the linearized local impulse response induced by quadratic roughness penalties depends on the object only through its projections. This analysis leads naturally to a modified regularization penalty that yields reconstructed images with nearly uniform resolution. The modified penalty also provides a very practical method for choosing the regularization parameter to obtain a specified resolution in images reconstructed by penalized-likelihood methods.

Spatial resolution properties of penalized-likelihood image reconstruction: space-invariant tomographs