Accelerated 3D image reconstruction with a morphological pyramid and noise-power convergence criterion

Abstract

Model-based iterative reconstruction (MBIR) for cone-beam CT (CBCT) offers better noise-resolution tradeoff and image quality than analytical methods for acquisition protocols with low x-ray dose or limited data, but with increased computational burden that poses a drawback to routine application in clinical scenarios. This work develops a comprehensive framework for acceleration of MBIR in the form of penalized weighted least squares optimized with ordered subsets separable quadratic surrogates. The optimization was scheduled on a set of stages forming a morphological pyramid varying in voxel size. Transition between stages was controlled with a convergence criterion based on the deviation between the mid-band noise power spectrum (NPS) measured on a homogeneous region of the evolving reconstruction and that expected for the converged image, computed with an analytical model that used projection data and the reconstruction parameters. A stochastic backprojector was developed by introducing a random perturbation to the sampling position of each voxel for each ray in the reconstruction within a voxel-based backprojector, breaking the deterministic pattern of sampling artifacts when combined with an unmatched Siddon forward projector. This fast, forward and backprojector pair were included into a multi-resolution reconstruction strategy to provide support for objects partially outside of the field of view. Acceleration from ordered subsets was combined with momentum accumulation stabilized with an adaptive technique that automatically resets the accumulated momentum when it diverges noticeably from the current iteration update. The framework was evaluated with CBCT data of a realistic abdomen phantom acquired on an imaging x-ray bench and with clinical CBCT data from an angiography robotic C-arm (Artis Zeego, Siemens Healthineers, Forchheim, Germany) acquired during a liver embolization procedure. Image fidelity was assessed with the structural similarity index (SSIM) computed with a converged reconstruction. The accelerated framework provided accurate reconstructions in 60 s (SSIM = 0.97) and as little as 27 s (SSIM = 0.94) for soft-tissue evaluation. The use of simple forward and backprojectors resulted in 9.3× acceleration. Accumulation of momentum provided extra ∼3.5× acceleration with stable convergence for 6–30 subsets. The NPS-driven morphological pyramid resulted in initial faster convergence, achieving similar SSIM with 1.5× lower runtime than the single-stage optimization. Acceleration of MBIR to provide reconstruction time compatible with clinical applications is feasible via architectures that integrate algorithmic acceleration with approaches to provide stable convergence, and optimization schedules that maximize convergence speed.

Spatiotemporal image reconstruction to enable high-frame-rate dynamic photoacoustic tomography with rotating-gantry volumetric imagers

“…29,35,36,40 It is important to note that previous studies have demonstrated that the combination of the OS approach with momentum schemes can lead to convergence instability, particularly as the number of subsets increases. 47,48,58,59 This instability arises due to error accumulation in the momentum term, as the "subset balance" approximation does not perfectly hold. 47 The "subset balance" approximation implies that the cost function, JðFÞ, defined in Eq.…”

“…Future refinements of the proposed method may explore the different strategies from the literature to obtain a provably convergent method. 48,58,59 Subsequent investigations may focus on evaluating the method's efficacy in imaging complex dynamic physiological processes and quantifying relevant parameters, such as wash-in and wash-out rates for tumor vascular perfusion. 37,60 These evaluations might encompass both in-vivo and in-silico experiments, further advancing the understanding and application of the proposed method.…”

Model-based three-material decomposition in dual-energy CT using the volume conservation constraint

“…The execution times are primarily affected by forward and back-projections of the volume (here, a total of 3 forward and 3 back-projections implemented per iteration) and the application of the spectral model. To address these bottlenecks, we are currently investigating: (i) multiresolution reconstruction that employs a finer voxel grid in the regions of interest (Cao et al 2016, Sisniega et al 2021, and (ii) polynomial approximation of the polyenergetic forward model (Abella et al 2019). Another important consideration for clinical translation is ensuring robust convergence of the algorithm.…”

Stationary x-ray tomography for hemorrhagic stroke imaging: sampling and resolution properties

“…The head was positioned with a 45° tilt along the z axis, aligning the central scan plane with a plane joining the posterior skull base with a frontal brain region. The x-ray source spectrum was simulated with the Spektr [10] TASMICS model for 100 kV (+2 mm Al, + 0.2 mm Cu added filtration). The detector model featured a flatpanel detector with a 250 mg/cm2 CsI:Tl scintillator.…”