Local and global 3D noise power spectrum in cone‐beam CT system with FDK reconstruction

Baek, Jongduk; Pelc, Norbert J.

doi:10.1118/1.3556590

Cited by 54 publications

(59 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This finding is in contrast to FBP reconstruction which carries uniform spatial resolution to the extent described by Eq. (9), recognizing the potential for nonuniform spatial resolution associated with sampling 13,14 and modified FDK algorithms with shift-variant filters. 50 The PSF at each voxel in a neighborhood N is assumed to be the same, or equivalently, the system is locally shift-invariant.…”

Section: -6mentioning

confidence: 99%

“…where S proj denotes the 2D projection NPS, Conversion gain from x-rays to secondary quanta (e.g., optical photons) P k Gain and spreading factors associated with K-fluorescence T 3 Transfer function due to stochastic spread of secondary quantā g 4 Coupling efficiency of photodiode a pd Width of (square) photodiode T 5 Transfer function due to photodiode aperture III 6 Detector pixel sampling (2D comb function) σ add Additive electronics noise III 8 Postreadout projection resampling (optional) T 8 Transfer function due to 2D binning aperture (optional) T 10 Ramp filter T 11 Apodization filter T 12 Interpolation filter T 13 Transfer function associated with backprojection of signal 13 Transfer function associated with backprojection of noise III 14 3D voxel sampling (3D comb function) III 15 Postreconstruction sampling (optional) T 15 Transfer function due to 3D binning aperture (optional) m Number of projections acquired across a circular orbit θ tot Total angular extent of acquisition M Magnification factor, source-detector distance (SDD)/source-axis distance (SAD) FOV Size of the reconstruction field of view…”

Section: B the Spatially-varying Nps And Mtf For Fbpmentioning

confidence: 99%

“…They furthermore quantified the difference between the diagonal and off-diagonal elements of the Fourier transform of the covariance matrix as a metric of stationarity. Baek and Pelc 13,14 studied nonstationary noise in fan-beam and cone-beam FBP reconstructions as a result of varying magnification, projection weighting, and cosine weighting, and quantified the NPS at different spatial locations within reconstructions of air and a water cylinder. Bartolac et al 15 investigated the nonstationary signal and noise characteristics in CBCT arising specifically from sampling along a circular source-detector trajectory (i.e., the spatially varying null cone associated with violation of Tuy's condition).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Task‐based detectability in CT image reconstruction by filtered backprojection and penalized likelihood estimation

et al. 2014

View full text Add to dashboard Cite

Purpose: Nonstationarity is an important aspect of imaging performance in CT and cone-beam CT (CBCT), especially for systems employing iterative reconstruction. This work presents a theoretical framework for both filtered-backprojection (FBP) and penalized-likelihood (PL) reconstruction that includes explicit descriptions of nonstationary noise, spatial resolution, and task-based detectability index. Potential utility of the model was demonstrated in the optimal selection of regularization parameters in PL reconstruction. Methods: Analytical models for local modulation transfer function (MTF) and noise-power spectrum (NPS) were investigated for both FBP and PL reconstruction, including explicit dependence on the object and spatial location. For FBP, a cascaded systems analysis framework was adapted to account for nonstationarity by separately calculating fluence and system gains for each ray passing through any given voxel. For PL, the point-spread function and covariance were derived using the implicit function theorem and first-order Taylor expansion according to Fessler ["Mean and variance of implicitly defined biased estimators (such as penalized maximum likelihood): Applications to tomography," IEEE Trans. Image Process. 5(3), 493-506 (1996)]. Detectability index was calculated for a variety of simple tasks. The model for PL was used in selecting the regularization strength parameter to optimize task-based performance, with both a constant and a spatially varying regularization map. Results: Theoretical models of FBP and PL were validated in 2D simulated fan-beam data and found to yield accurate predictions of local MTF and NPS as a function of the object and the spatial location. The NPS for both FBP and PL exhibit similar anisotropic nature depending on the pathlength (and therefore, the object and spatial location within the object) traversed by each ray, with the PL NPS experiencing greater smoothing along directions with higher noise. The MTF of FBP is isotropic and independent of location to a first order approximation, whereas the MTF of PL is anisotropic in a manner complementary to the NPS. Task-based detectability demonstrates dependence on the task, object, spatial location, and smoothing parameters. A spatially varying regularization "map" designed from locally optimal regularization can improve overall detectability beyond that achievable with the commonly used constant regularization parameter. Conclusions: Analytical models for task-based FBP and PL reconstruction are predictive of nonstationary noise and resolution characteristics, providing a valuable framework for understanding and optimizing system performance in CT and CBCT.

show abstract

Section: -6mentioning

confidence: 99%

Section: B the Spatially-varying Nps And Mtf For Fbpmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Task‐based detectability in CT image reconstruction by filtered backprojection and penalized likelihood estimation

et al. 2014

View full text Add to dashboard Cite

show abstract

“…[71][72][73] These effects would need to be studied in the future, although experimental results presented in this work suggest that their effects may be negligible.…”

Section: Discussionmentioning

confidence: 99%

Fundamental relationship between the noise properties of grating-based differential phase contrast CT and absorption CT: Theoretical framework using a cascaded system model and experimental validation

Bevins

Zambelli

et al. 2013

Med. Phys.

View full text Add to dashboard Cite

Purpose: Using a grating interferometer, a conventional x-ray cone beam computed tomography (CT) data acquisition system can be used to simultaneously generate both conventional absorption CT (ACT) and differential phase contrast CT (DPC-CT) images from a single data acquisition. Since the two CT images were extracted from the same set of x-ray projections, it is expected that intrinsic relationships exist between the noise properties of the two contrast mechanisms. The purpose of this paper is to investigate these relationships. Methods: First, a theoretical framework was developed using a cascaded system model analysis to investigate the relationship between the noise power spectra (NPS) of DPC-CT and ACT. Based on the derived analytical expressions of the NPS, the relationship between the spatial-frequencydependent noise equivalent quanta (NEQ) of DPC-CT and ACT was derived. From these fundamental relationships, the NPS and NEQ of the DPC-CT system can be derived from the corresponding ACT system or vice versa. To validate these theoretical relationships, a benchtop cone beam DPC-CT/ACT system was used to experimentally measure the modulation transfer function (MTF) and NPS of both DPC-CT and ACT. The measured three-dimensional (3D) MTF and NPS were then combined to generate the corresponding 3D NEQ. Results: Two fundamental relationships have been theoretically derived and experimentally validated for the NPS and NEQ of DPC-CT and ACT: (1) the 3D NPS of DPC-CT is quantitatively related to the corresponding 3D NPS of ACT by an inplane-only spatial-frequency-dependent factor 1/f 2 , the ratio of window functions applied to DPC-CT and ACT, and a numerical factor C g determined by the geometry and efficiency of the grating interferometer. Note that the frequency-dependent factor is independent of the frequency component f z perpendicular to the axial plane. (2) The 3D NEQ of DPC-CT is related to the corresponding 3D NEQ of ACT by an f 2 scaling factor and numerical factors that depend on both the attenuation and refraction properties of the image object, as well as C g and the MTF of the grating interferometer. Conclusions: The performance of a DPC-CT system is intrinsically related to the corresponding ACT system. As long as the NPS and NEQ of an ACT system is known, the corresponding NPS and NEQ of the DPC-CT system can be readily estimated using additional characteristics of the grating interferometer.

show abstract

“…It is a fundamental understanding that the subject contrast of soft tissues in an imaging system is intrinsically determined by their interaction with the x-ray beam, [14][15][16] while the system's performance is determined by its signal and noise transfer properties. 11,[17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] In principle, the signal transfer property of an imaging system is dependent on its modulation transfer function MTF(k), [17][18][19][20][21][22][23][24][25][26][27][28][29][30] while the noise transfer property can only be thoroughly characterized by its noise power spectrum NPS(k), i.e., the variation of noise intensity as a function over spatial frequency k. [17][18][19][20][21][22][23][24][25]…”

Section: Introductionmentioning

confidence: 99%

Characterization of imaging performance in differential phase contrast CT compared with the conventional CT: Spectrum of noise equivalent quanta NEQ( k )

2012

View full text Add to dashboard Cite

Purpose: Differential phase contrast CT (DPC-CT) is emerging as a new technology to improve the contrast sensitivity of conventional attenuation-based CT. The noise equivalent quanta as a function over spatial frequency, i.e., the spectrum of noise equivalent quanta NEQ(k), is a decisive indicator of the signal and noise transfer properties of an imaging system. In this work, we derive the functional form of NEQ(k) in DPC-CT. Via system modeling, analysis, and computer simulation, we evaluate and verify the derived NEQ(k) and compare it with that of the conventional attenuation-based CT. Methods: The DPC-CT is implemented with x-ray tube and gratings. The x-ray propagation and data acquisition are modeled and simulated through Fresnel and Fourier analysis. A monochromatic x-ray source (30 keV) is assumed to exclude any system imperfection and interference caused by scatter and beam hardening, while a 360• full scan is carried out in data acquisition to avoid any weighting scheme that may disrupt noise randomness. Adequate upsampling is implemented to simulate the x-ray beam's propagation through the gratings G 1 and G 2 with periods 8 and 4 μm, respectively, while the intergrating distance is 193.6 mm (1/16 of the Talbot distance). The dimensions of the detector cell for data acquisition are 32 × 32, 64 × 64, 96 × 96, and 128 × 128 μm 2 , respectively, corresponding to a 40.96 × 40.96 mm 2 field of view in data acquisition. An air phantom is employed to obtain the noise power spectrum NPS(k), spectrum of noise equivalent quanta NEQ(k), and detective quantum efficiency DQE(k). A cylindrical water phantom at 5.1 mm diameter and complex refraction coefficient n = 1 − δ + iβ = 1 −2.5604 × 10 −7 + i1.2353 × 10 −10 is placed in air to measure the edge transfer function, line spread function and then modulation transfer function MTF(k), of both DPC-CT and the conventional attenuation-based CT. The x-ray flux is set at 5 × 10 6 photon/cm 2 per projection and observes the Poisson distribution, which is consistent with that of a micro-CT for preclinical applications. Approximately 360 regions, each at 128 × 128 matrix, are used to calculate the NPS(k) via 2D Fourier transform, in which adequate zero padding is carried out to avoid aliasing in noise. Results:The preliminary data show that the DPC-CT possesses a signal transfer property [MTF(k)] comparable to that of the conventional attenuation-based CT. Meanwhile, though there exists a radical difference in their noise power spectrum NPS(k) (trait 1/|k| in DPC-CT but |k| in the conventional attenuation-based CT) the NEQ(k) and DQE(k) of DPC-CT and the conventional attenuation-based CT are in principle identical. Conclusions: Under the framework of ideal observer study, the joint signal and noise transfer property NEQ(k) and detective quantum efficiency DQE(k) of DPC-CT are essentially the same as those of the conventional attenuation-based CT. The findings reported in this paper may provide insightful guidelines on the research, development, and performance optimization o...

show abstract

Local and global 3D noise power spectrum in cone‐beam CT system with FDK reconstruction

Cited by 54 publications

References 35 publications

Task‐based detectability in CT image reconstruction by filtered backprojection and penalized likelihood estimation

Task‐based detectability in CT image reconstruction by filtered backprojection and penalized likelihood estimation

Fundamental relationship between the noise properties of grating-based differential phase contrast CT and absorption CT: Theoretical framework using a cascaded system model and experimental validation

Characterization of imaging performance in differential phase contrast CT compared with the conventional CT: Spectrum of noise equivalent quanta NEQ( k )

Contact Info

Product

Resources

About