An expression for the noise power spectrum of images reconstructed by the discrete filtered backprojection algorithm has been derived. The formulation explicitly includes sampling within the projections, angular sampling, and the two-dimensional sampling implicit in the discrete representation of the image. The effects of interpolation are also considered. Noise power spectra predicted by this analysis differ from those predicted using continuous theory in two respects: they are rotationally asymmetric, and they do not approach zero at zero frequency. Both of these properties can be attributed to two-dimensional aliasing due to pixel sampling. The predictions were confirmed by measurement of noise power spectra of both simulated images and images from a commercial x-ray transmission CT scanner.

https://iopscience.iop.org/article/10.1088/0031-9155/32/5/003/pdf

The noise power spectrum of CT images

Dose reduction efforts in diagnostic CT have brought the tradeoff of dose versus image quality to the forefront. The need for meaningful characterization of image noise beyond that offered by pixel standard deviation is becoming increasingly important. This work aims to study the implementation of the noise power spectrum (NPS) and noise equivalent quanta (NEQ) on modern, multislice diagnostic CT scanners. The details of NPS and NEQ measurement are outlined and special attention is paid to issues unique to multislice CT. Aliasing, filter design and effects of acquisition geometry are investigated. While it was found that both metrics can be implemented in modern CT, it was discovered that NEQ cannot be aptly applied with certain non-traditional reconstruction filters or in helical mode. NPS and NEQ under a variety of conditions are examined. Extensions of NPS and NEQ to uses in protocol standardization are also discussed.

https://iopscience.iop.org/article/10.1088/0031-9155/52/14/002/pdf

Application of the noise power spectrum in modern diagnostic MDCT: part I. Measurement of noise power spectra and noise equivalent quanta.

The physical factors that govern 2D and 3D imaging performance may be understood from quantitative analysis of the spatial-frequency-dependent signal and noise transfer characteristics [e.g., modulation transfer function (MTF), noise-power spectrum (NPS), detective quantum efficiency (DQE), and noise-equivalent quanta (NEQ)] along with a task-based assessment of performance (e.g., detectability index). This paper advances a theoretical framework based on cascaded systems analysis for calculation of such metrics in cone-beam CT (CBCT). The model considers the 2D projection NPS propagated through a series of reconstruction stages to yield the 3D NPS and allows quantitative investigation of tradeoffs in image quality associated with acquisition and reconstruction techniques. While the mathematical process of 3D image reconstruction is deterministic, it is shown that the process is irreversible, the associated reconstruction parameters significantly affect the 3D DQE and NEQ, and system optimization should consider the full 3D imaging chain. Factors considered in the cascade include: system geometry; number of projection views; logarithmic scaling; ramp, apodization, and interpolation filters; 3D back-projection; and 3D sampling (noise aliasing). The model is validated in comparison to experiment across a broad range of dose, reconstruction filters, and voxel sizes, and the effects of 3D noise correlation on detectability are explored. The work presents a model for the 3D NPS, DQE, and NEQ of CBCT that reduces to conventional descriptions of axial CT as a special case and provides a fairly general framework that can be applied to the design and optimization of CBCT systems for various applications.

/pdf/cascaded-systems-analysis-of-the-3d-noise-transfer-4nrhwhq6ho.pdf

Cascaded systems analysis of the 3D noise transfer characteristics of flat-panel cone-beam CT

The optimization of digital breast tomosynthesis (DBT) geometry and reconstruction is crucial for the clinical translation of this exciting new imaging technique. In the present work, the authors developed a three-dimensional (3D) cascaded linear system model for DBT to investigate the effects of detector performance, imaging geometry, and image reconstruction algorithm on the reconstructed image quality. The characteristics of a prototype DBT system equipped with an amorphous selenium flat-panel detector and filtered backprojection reconstruction were used as an example in the implementation of the linear system model. The propagation of signal and noise in the frequency domain was divided into six cascaded stages incorporating the detector performance, imaging geometry, and reconstruction filters. The reconstructed tomosynthesis imaging quality was characterized by spatial frequency dependent presampling modulation transfer function (MTF), noise power spectrum (NPS), and detective quantum efficiency (DQE) in 3D. The results showed that both MTF and NPS were affected by the angular range of the tomosynthesis scan and the reconstruction filters. For image planes parallel to the detector (in-plane), MTF at low frequencies was improved with increase in angular range. The shape of the NPS was affected by the reconstruction filters. Noise aliasing in 3D could be introduced by insufficient voxel sampling, especially in the z (slice-thickness) direction where the sampling distance (slice thickness) could be more than ten times that for in-plane images. Aliasing increases the noise at high frequencies, which causes degradation in DQE. Application of a reconstruction filter that limits the frequency components beyond the Nyquist frequency in the z direction, referred to as the slice thickness filter, eliminates noise aliasing and improves 3D DQE. The focal spot blur, which arises from continuous tube travel during tomosynthesis acquisition, could degrade DQE significantly because it introduces correlation in signal only, not NPS.

Three-dimensional linear system analysis for breast tomosynthesis

Balancing dose and image quality requires signal-to-noise (SNR) metrics which incorporate both the variance and the spatial frequency characteristics of noise In this study, the non-prewhitening matched filter SNR metric is calculated for 2 mm slices of a 1 cm diameter sphere under three different conditions: (1) constant pixel standard deviation, (2) constant dose and (3) constant reconstruction filter For the constant pixel standard deviation condition, an increase of 260% in SNR was found with increasing filter sharpness For constant dose, the SNR remained level for smooth to medium filters, then declined by up to 55% with increasing filter sharpness For a constant reconstruction filter, the SNR increased with dose, but not as high as photon statistics would predict However, when structured noise was removed from the noise power spectrum, the SNR did vary with quanta statistics These results offer protocol design guidance for low-frequency-dominated objects

https://iopscience.iop.org/article/10.1088/0031-9155/52/14/003/pdf

Application of the noise power spectrum in modern diagnostic MDCT: part II. Noise power spectra and signal to noise.

A discrete representation of the reconstruction process, consistent with the method of data collection, has been used to derive expressions for the noise power spectrum, autocorrelation function and noise equivalent quanta (NEQ) of a computed tomography (CT) image. These parameters have been expressed in terms of basic scanning factors such as tube current, exposure time, slice width and number of detectors. Each of these factors affects the overall magnitude of the noise power spectrum, but the spatial frequency dependence is also determined by the type of reconstruction filter used in the computer algorithm. The noise power spectrum has been calculated for scanners employing either a ramp or Hanning weighted ramp filter. Predictions made from this theoretical analysis have been compared with experimental measurements made on various CT scanners. Measurements were made of the modulation transfer function (MTF) by techniques which permitted us to deduce the contributions of the algorithmic and non-algorithmic components to the overall MTF. NEQ values have been calculated for a number of CT scanners.

https://iopscience.iop.org/article/10.1088/0031-9155/29/11/003/pdf

K Faulkner

Papers

Analysis of x-ray computed tomography images using the noise power spectrum and autocorrelation function.