Analysis of Fourier‐domain task‐based detectability index in tomosynthesis and cone‐beam CT in relation to human observer performance

Abstract

Design and optimization of medical imaging systems benefit from accurate theoretical modeling that identifies the physical factors governing image quality, particularly in the early stages of system development. This work extends Fourier metrics of imaging performance and detectability index (d') to tomosynthesis and cone-beam CT (CBCT) and investigates the extent to which d' is a valid descriptor of task-based imaging performance as assessed by human observers, The detectability index for tasks presented in 2D slices (d'(slice)) was derived from 3D cascaded systems analysis of tomosynthesis and CBCT. Anatomical background noise measured in a physical phantom presenting power-law spectral density was incorporated in the "generalized" noise-equivalent quanta. Theoretical calculations of d'(slice) were performed as a function of total angular extent (theta(tot)) of source-detector orbit ranging 10 degrees - 360 degrees under two acquisition schemes: (i) Constant angular separation between projections (constant-delta theta), giving variable number of projections (N(proj)) and dose vs theta(tot) and (ii) constant number of projections (constant-N(proj)), giving constant dose (but variable angular sampling) with theta(tot). Five simple observer models were investigated: Prewhitening (PW), prewhitening with eye filter and internal noise (PWEi), nonprewhitening (NPW), nonprewhitening with eye filter (NPWE), and nonprewhitening with eye filter and internal noise (NPWEi). Human observer performance was measured in 9AFC tests for five simple imaging tasks presented within uniform and power-law clutter backgrounds. Measurements (from 9AFC tests) and theoretical calculations (from cascaded systems analysis of d'(slice)) were compared in terms of area under the ROC curve (A(z)) Reasonable correspondence between theoretical calculations and human observer performance was achieved for all imaging tasks over the broad range of experimental conditions and acquisition schemes. The PW and PWEi observer models tended to overestimate detectability, while the various NPW models predicted observer performance fairly well, with NPWEi giving the best overall agreement. Detectability was shown to increase with theta(tot) due to the reduction of out-of-plane clutter, reaching a plateau after a particular theta(tot) that depended on the imaging task. Depending on the acquisition scheme, however (i.e., constant-N(proj) or delta theta), detectability was seen in some cases to decline at higher theta(tot) due to tradeoffs among quantum noise, background clutter, and view sampling. Generalized detectability index derived from a 3D cascaded systems model shows reasonable correspondence with human observer performance over a fairly broad range of imaging tasks and conditions, although discrepancies were observed in cases relating to orbits intermediate to 180 degrees and 360 degrees. The basic correspondence of theoretical and measured performance supports the application of such a theoretical framework for system design and optimization of tomosynthesis and CBCT.