Quantitative Statistical Methods for Image Quality Assessment

Abstract

Quantitative measures of image quality and reliability are critical for both qualitative interpretation and quantitative analysis of medical images. While, in theory, it is possible to analyze reconstructed images by means of Monte Carlo simulations using a large number of noise realizations, the associated computational burden makes this approach impractical. Additionally, this approach is less meaningful in clinical scenarios, where multiple noise realizations are generally unavailable. The practical alternative is to compute closed-form analytical expressions for image quality measures. The objective of this paper is to review statistical analysis techniques that enable us to compute two key metrics: resolution (determined from the local impulse response) and covariance. The underlying methods include fixed-point approaches, which compute these metrics at a fixed point (the unique and stable solution) independent of the iterative algorithm employed, and iteration-based approaches, which yield results that are dependent on the algorithm, initialization, and number of iterations. We also explore extensions of some of these methods to a range of special contexts, including dynamic and motion-compensated image reconstruction. While most of the discussed techniques were developed for emission tomography, the general methods are extensible to other imaging modalities as well. In addition to enabling image characterization, these analysis techniques allow us to control and enhance imaging system performance. We review practical applications where performance improvement is achieved by applying these ideas to the contexts of both hardware (optimizing scanner design) and image reconstruction (designing regularization functions that produce uniform resolution or maximize task-specific figures of merit).

Estimation of noise properties for TV-regularized image reconstruction in computed tomography

“…Additionally, the same work provided asymptotic analysis of noise properties so that the propagation-based approach could be bridged to the other major method, which we refer to as a fixed-point method, since it analyses noise properties at the fixed point of the objective function. The basic approach for fixed-point noise analysis was presented by Fessler [46], with subsequent development and application still ongoing [47]–[52]. In particular, Refs.…”

“…In particular, Refs. [50] and [52] clarify the relationship between iteration-based methods and fixed-point methods. Additionally, Ref.…”

Task‐based detectability in CT image reconstruction by filtered backprojection and penalized likelihood estimation

“…[21][22][23][24] Efforts toward task-based assessment and optimization of statistical reconstruction have mostly been concentrated in emission tomography. [25][26][27][28][29][30][31][32][33][34][35][36][37] The work reported below investigates the nonstationary noise, resolution, and task-based performance in CBCT reconstructed with both FBP and statistical algorithms. For the latter, the current analysis pertains to penalized likelihood (PL) estimation with a quadratic penalty.…”

Pulmonary imaging using respiratory motion compensated simultaneous PET/MR

“…Additionally, it is feasible to derive closed form estimates of the resolution and variance of the MAP estimate for further statistical analysis. [75][76][77][78] We have also proposed and validated a strategy for regularization parameter selection based on consistent relative weighting of the data-fit and regularizer terms for the OG, UG, and MC cases. In the absence of consistent weighting, corresponding voxels could have arbitrary resolution and variance properties, making both quantitative and qualitative comparison of the three cases less meaningful.…”