A modified uniform Cramer-Rao bound for multiple pinhole aperture design

This paper presents a modified Uniform Cramer-Rao bound (UCRB) for studying estimator spatial resolution and variance tradeoffs. We proposed to use a resolution constraint that is imposed on mean gradient vectors of achieved estimators and derived the minimum achievable variance for any estimator satisfies this resolution constraint. This approach partially overcomes the limitations of the former UCRB approach based on a bias-gradient norm constraint. We applied this method in a feasibility study of using multiple pinhole apertures for small animal SPECT imaging applications. The SPECT system studied was based on an existing gamma camera. The achievable spatial resolution and variance tradeoffs for systems with different design parameters, such as number of pinholes and pinhole size, were studied.