Statistical x-ray computed tomography imaging from photon-starved measurements

Predicting noise properties of iteratively reconstructed CT images is useful for analyzing reconstruction methods; for example, local noise power spectrum (NPS) predictions may be used to quantify the detectability of an image feature, to design regularization methods, or to determine dynamic tube current adjustment during a CT scan. This paper presents a method for fast prediction of reconstructed image variance and local NPS for statistical reconstruction methods using quadratic or locally quadratic regularization. Previous methods either require impractical computation times to generate an approximate map of the variance of each reconstructed voxel, or are restricted to specific CT geometries. Our method can produce a variance map of the entire image, for locally shift-invariant CT geometries with sufficiently fine angular sampling, using a computation time comparable to a single back-projection. The method requires only the projection data to be used in the reconstruction, not a reconstruction itself, and is reasonably accurate except near image edges where edge-preserving regularization behaves highly nonlinearly. We evaluate the accuracy of our method using reconstructions of both simulated CT data and real CT scans of a thorax phantom.

Section: Resultsmentioning

confidence: 99%

Fast Variance Prediction for Iteratively Reconstructed CT Images With Locally Quadratic Regularization

Schmitt

Goodsitt

Fessler

2017

“…The tube current and tube voltage of the X-ray source are 750 mA and 120 kVp, respectively. We started from a smoothed FBP image x (0) and tuned the statistical weights [36] and the q -generalized Gaussian MRF regularization parameters [33] to emulate the MBIR method [3, 37]. We used 10 subsets for the relaxed OS-LALM, while [11, Eqn.…”

Section: Resultsmentioning

confidence: 99%

Relaxed Linearized Algorithms for Faster X-Ray CT Image Reconstruction

Nien

Fessler

2016

Statistical image reconstruction (SIR) methods are studied extensively for X-ray computed tomography (CT) due to the potential of acquiring CT scans with reduced X-ray dose while maintaining image quality. However, the longer reconstruction time of SIR methods hinders their use in X-ray CT in practice. To accelerate statistical methods, many optimization techniques have been investigated. Over-relaxation is a common technique to speed up convergence of iterative algorithms. For instance, using a relaxation parameter that is close to two in alternating direction method of multipliers (ADMM) has been shown to speed up convergence significantly. This paper proposes a relaxed linearized augmented Lagrangian (AL) method that shows theoretical faster convergence rate with over-relaxation and applies the proposed relaxed linearized AL method to X-ray CT image reconstruction problems. Experimental results with both simulated and real CT scan data show that the proposed relaxed algorithm (with ordered-subsets [OS] acceleration) is about twice as fast as the existing unrelaxed fast algorithms, with negligible computation and memory overhead.

“…Directly using y i to compute W i causes strong statistical correlation between W i and p i . In practice, smoothed or de-noised data can be used instead [38][31][36][32]. As an example, we implement a locally adaptive linear minimum mean squared-error (LLMMSE) filter very similar to what proposed by Chang, Zhang, Thibault, et al [78], where denoised data ӯ i , p̄ i and W̄ i , are used instead of the noisy data y i , p i , and W i .…”

Section: Statistical Modelsmentioning

confidence: 99%

“…These non-positive values must be either zero-weighted [30], replaced by some artificial positive values [17], corrected by some recursive mean-preserving operations [31], or interpolated by some sinogram smoothing or denoising methods [6], [32]–[35]. For example, Chang, Zhang, and Thibault [36] proposed a Bayesian inference method to map non-positive transmission measurements to positive values. However, when the extent of such pre-correction is aggressive, such as in ultra-low-dose CT, bias could be introduced in the reconstructed image and spatial resolution could be degraded.…”

Section: Introductionmentioning

confidence: 99%

“…Estimation of the weights is challenging due to the correction of non-positive values and the non-linearity of the logarithm [37]. Examples of existing variance estimation techniques include noisy-data based weights [14], [21], [24], [38], denoised-data based weights [31], [32], [36], [38], model-based weights using certain mean-variance relationship [39][10][40], and iteratively re-weighted least-squares [17], [29], [41]. Also, statistical correlation between the estimated weights and the noisy data can cause negative bias in the reconstructed image [15], [38], [39].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Comparison Between Pre-Log and Post-Log Statistical Models in Ultra-Low-Dose CT Reconstruction

Lee

Kim

et al. 2017

Self Cite

X-ray detectors in clinical computed tomography (CT) usually operate in current-integrating mode. Their complicated signal statistics often lead to intractable likelihood functions for practical use in model-based image reconstruction (MBIR). It is therefore desirable to design simplified statistical models without losing the essential factors. Depending on whether the CT transmission data are logarithmically transformed, pre-log and post-log models are two major categories of choices in CT MBIR. Both being approximations, it remains an open question whether one model can notably improve image quality over the other on real scanners. In this study, we develop and compare several pre-log and post-log MBIR algorithms under a unified framework. Their reconstruction accuracy based on simulation and clinical datasets are evaluated. The results show that pre-log MBIR can achieve notably better quantitative accuracy than post-log MBIR in ultra-low-dose CT, although in less extreme cases, post-log MBIR with handcrafted pre-processing remains a competitive alternative. Pre-log MBIR could play a growing role in emerging ultra-low-dose CT applications.