Resolution Properties of Regularized Image Reconstruction Methods

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-variantlocal 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.

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