Analytic noise-propagation in indirect fan-beam FBP reconstruction

Analytical covariance estimation for iterative CT reconstruction methods

Covariance of reconstruction images are useful to analyze the magnitude and correlation of noise in the evaluation of systems and reconstruction algorithms. The covariance estimation requires a big number of image samples that are hard to acquire in reality. A covariance propagation method from projection by a few noisy realizations is studied in this work. Based on the property of convergent points of cost funtions, the proposed method is composed of three steps, (1) construct a relationship between the covariance of projection and corresponding reconstruction from cost functions at its convergent point, (2) simplify the covariance relationship constructed in (1) by introducing an approximate gradient of penalties, and (3) obtain an analytical covariance estimation according to the simplified relationship in (2). Three approximation methods for step (2) are studied: the linear approximation of the gradient of penalties (LAM), the Taylor apprximation (TAM), and the mixture of LAM and TAM (MAM). TV and qGGMRF penalized weighted least square methods are experimented on. Results from statistical methods are used as reference. Under the condition of unstable 2nd derivative of penalties such as TV, the covariance image estimated by LAM accords to reference well but of smaller values, while the covarianc estimation by TAM is quite off. Under the conditon of relatively stable 2nd derivative of penalties such as qGGMRF, TAM performs well and LAM is again with a negative bias in magnitude. MAM gives a best performance under both conditions by combining LAM and TAM. Results also show that only one noise realization is enough to obtain reasonable covariance estimation analytically, which is important for practical usage. This work suggests the necessity and a new way to estimate the covariance for non-quadratically penalized reconstructions. Currently, the proposed method is computationally expensive for large size reconstructions.Computational efficiency is our future work to focus.

Estimation of signal and noise for a whole-body research photon-counting CT system

Photon-counting detector CT has a large number of acquisition parameters that require optimization, particularly the energy threshold configurations. Fast and accurate estimation of both signal and noise in photon-counting CT (PCCT) images can facilitate such optimization. Using the detector response function of a research PCCT system, we derived mathematical models for both signal and noise estimation, taking into account beam spectrum and filtration, object attenuation, water beam hardening, detector response, radiation dose, energy thresholds, and the propagation of noise. To determine the absolute noise value, a noise lookup table (LUT) for all available energy thresholds was acquired using a number of calibration scans. The noise estimation algorithm then used the noise LUT to estimate noise for scans with a variety of combination of energy thresholds, dose levels, and object attenuations. Validation of the estimation algorithms was performed on a whole-body research PCCT system using semianthropomorphic water phantoms and solutions of calcium and iodine. Clinical feasibility of noise estimation was assessed with scans of a cadaver head and a living swine. The algorithms achieved accurate estimation of both signal and noise for a variety of scanning parameter combinations. Maximum discrepancies were below 15%, while most errors were below 5%.

Statistical characterization of noise for spatial standardization of CT scans: Enabling comparison with multiple kernels and doses

Computerized tomography (CT) is a widely adopted modality for analyzing directly or indirectly functional, biological and morphological processes by means of the image characteristics. However, the potential utilization of the information obtained from CT images is often limited when considering the analysis of quantitative information involving different devices, acquisition protocols or reconstruction algorithms. Although CT scanners are calibrated as a part of the imaging workflow, the calibration is circumscribed to global reference values and does not circumvent problems that are inherent to the imaging modality. One of them is the lack of noise stationarity, which makes quantitative biomarkers extracted from the images less robust and stable. Some methodologies have been proposed for the assessment of non-stationary noise in reconstructed CT scans. However, those methods focused on the non-stationarity only due to the reconstruction geometry and are mainly based on the propagation of the variance of noise throughout the whole reconstruction process. Additionally, the philosophy followed in the state-of-the-art methods is based on the reduction of noise, but not in the standardization of it. This means that, even if the noise is reduced, the statistics of the signal remain non-stationary, which is insufficient to enable comparisons between different acquisitions with different statistical characteristics. In this work, we propose a statistical characterization of noise in reconstructed CT scans that leads to a versatile statistical model that effectively characterizes different doses, reconstruction kernels, and devices. The statistical model is generalized to deal with the partial volume effect via a localized mixture model that also describes the non-stationarity of noise. Finally, we propose a stabilization scheme to achieve stationary variance. The validation of the proposed methodology was performed with a physical phantom and clinical CT scans acquired with different configurations (kernels, doses, algorithms including iterative reconstruction). The results confirmed its suitability to enable comparisons with different doses, and acquisition protocols.

Three-dimensional anisotropic adaptive filtering of projection data for noise reduction in cone beam CT

PURPOSE

The combination of quickly rotating C-arm gantry with digital flat panel has enabled the acquisition of three-dimensional data (3D) in the interventional suite. However, image quality is still somewhat limited since the hardware has not been optimized for CT imaging. Adaptive anisotropic filtering has the ability to improve image quality by reducing the noise level and therewith the radiation dose without introducing noticeable blurring. By applying the filtering prior to 3D reconstruction, noise-induced streak artifacts are reduced as compared to processing in the image domain.

METHODS

3D anisotropic adaptive filtering was used to process an ensemble of 2D x-ray views acquired along a circular trajectory around an object. After arranging the input data into a 3D space (2D projections + angle), the orientation of structures was estimated using a set of differently oriented filters. The resulting tensor representation of local orientation was utilized to control the anisotropic filtering. Low-pass filtering is applied only along structures to maintain high spatial frequency components perpendicular to these. The evaluation of the proposed algorithm includes numerical simulations, phantom experiments, and in-vivo data which were acquired using an AXIOM Artis dTA C-arm system (Siemens AG, Healthcare Sector, Forchheim, Germany). Spatial resolution and noise levels were compared with and without adaptive filtering. A human observer study was carried out to evaluate low-contrast detectability.

RESULTS

The adaptive anisotropic filtering algorithm was found to significantly improve low-contrast detectability by reducing the noise level by half (reduction of the standard deviation in certain areas from 74 to 30 HU). Virtually no degradation of high contrast spatial resolution was observed in the modulation transfer function (MTF) analysis. Although the algorithm is computationally intensive, hardware acceleration using Nvidia's CUDA Interface provided an 8.9-fold speed-up of the processing (from 1336 to 150 s).

CONCLUSIONS

Adaptive anisotropic filtering has the potential to substantially improve image quality and/or reduce the radiation dose required for obtaining 3D image data using cone beam CT.

Band-restricted estimation of noise variance in filtered backprojection reconstructions using repeated scans

We introduce a new estimator for noise variance in tomographic images reconstructed using algorithms of the filtered backprojection type. The new estimator operates on data acquired from repeated scans of the object under examination, is unbiased, and is shown to have significantly lower variance than the conventional unbiased estimator for many scenarios of practical interest. We provide an extensive theoretical analysis of this estimator, highlighting the circumstances under which it is most effective. This analysis includes both general and specific data-correlation patterns. Moreover, we have applied our estimator to real X-ray computed tomography data and present preliminary results that support the theory and provide experimental evidence of the new estimator's efficacy.