Reconstruction-Aware Imaging System Ranking by use of a Sparsity-Driven Numerical Observer Enabled by Variational Bayesian Inference

It is widely accepted that optimization of imaging system performance should be guided by task-based measures of image quality (IQ). It has been advocated that imaging hardware or data-acquisition designs should be optimized by use of an ideal observer (IO) that exploits full statistical knowledge of the measurement noise and class of objects to be imaged, without consideration of the reconstruction method. In practice, accurate and tractable models of the complete object statistics are often difficult to determine. Moreover, in imaging systems that employ compressive sensing concepts, imaging hardware and sparse image reconstruction are innately coupled technologies. In this work, a sparsity-driven observer (SDO) that can be employed to optimize hardware by use of a stochastic object model describing object sparsity is described and investigated. The SDO and sparse reconstruction method can therefore be "matched" in the sense that they both utilize the same statistical information regarding the class of objects to be imaged. To efficiently compute the SDO test statistic, computational tools developed recently for variational Bayesian inference with sparse linear models are adopted. The use of the SDO to rank data-acquisition designs in a stylized example as motivated by magnetic resonance imaging (MRI) is demonstrated. This study reveals that the SDO can produce rankings that are consistent with visual assessments of the reconstructed images but different from those produced by use of the traditionally employed Hotelling observer (HO).