The noise power spectrum in CT with direct fan beam reconstruction

Baek, Jongduk; Pelc, Norbert J.

doi:10.1118/1.3378673

Cited by 66 publications

(66 citation statements)

References 27 publications

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“…As was demonstrated by Baek and Pelc, 61 the noise is nonstationary for images reconstructed from fan-beam projection data using an FBP reconstruction algorithm. Consequently, the NPS varies for different positions within the image.…”

Section: Viib Resultsmentioning

confidence: 84%

“…When dealing with correlated noise, the NPW observer model has been shown to approximate human observers more accurately than pre-whitening models. [53][54][55][56][57][58][59] CT images have correlated noise due to the reconstruction procedure 60,61 and thus, a NPW observer model is expected to be more consistent with a human observer. 62 Furthermore, the noise of CT images is often non-stationary, 61 i.e., it varies spatially.…”

Section: Vb Model Observer Detection Taskmentioning

confidence: 99%

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Characterization of statistical prior image constrained compressed sensing. I. Applications to time‐resolved contrast‐enhanced CT

Thériault-Lauzier

Chen

2012

Medical Physics

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Purpose: Prior image constrained compressed sensing (PICCS) is an image reconstruction framework that takes advantage of a prior image to improve the image quality of CT reconstructions. An interesting question that remains to be investigated is whether or not the introduction of a statistical model of the photon detection in the PICCS reconstruction framework can improve the performance of the algorithm when dealing with high noise projection datasets. The goal of the research presented in this paper is to characterize the noise properties of images reconstructed using PICCS with and without statistical modeling. This paper investigates these properties in the clinical context of timeresolved contrast-enhanced CT. Methods: Both numerical phantom studies and an Institutional Review Board approved human subject study were used in this research. The conventional filtered backprojection (FBP), and PICCS with and without the statistical model were applied to each dataset. The prior image used in PICCS was generated by averaging over FBP reconstructions from different time frames of the time-resolved CT exam, thus reducing the noise level. Numerical studies were used to evaluate if the noise characteristics are altered for varying levels of noise, as well as for different object shapes. The dataset acquired in vivo was used to verify that the conclusions reached from numerical studies translate adequately to a clinical case. The results were analyzed using a variety of qualitative and quantitative metrics such as the universal image quality index, spatial maps of the noise standard deviations, the noise uniformity, the noise power spectrum, and the model-observer detectability. Results:The noise characteristics of PICCS were shown to depend on the noise level contained in the data, the level of eccentricity of the object, and whether or not the statistical model was applied. Most differences in the characteristics were observed in the regime of low incident x-ray fluence. No substantial difference was observed between PICCS with and without statistics in the high fluence domain. Objects with a semi-major axis ratio below 0.85 were more accurately reconstructed with lower noise using the statistical implementation. Above that range, for mostly circular objects, the PICCS implementation without the statistical model yielded more accurate images and a lower noise level. At all levels of eccentricity, the noise spatial distribution was more uniform and the modelobserver detectability was greater for PICCS with the statistical model. The human subject study was consistent with the results obtained using numerical simulations. Conclusions: For mildly eccentric objects in the low noise regime, PICCS without the noise model yielded equal or better noise level and image quality than the statistical formulation. However, in a vast majority of cases, images reconstructed using statistical PICCS have a noise power spectrum that facilitated the detection of model lesions. The inclusion of a statistical model in the PICCS framewor...

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Section: Viib Resultsmentioning

confidence: 84%

Section: Vb Model Observer Detection Taskmentioning

confidence: 99%

Characterization of statistical prior image constrained compressed sensing. I. Applications to time‐resolved contrast‐enhanced CT

Thériault-Lauzier

Chen

2012

Medical Physics

View full text Add to dashboard Cite

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“…[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.

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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.

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“…27,33,34 The slice of the Catphan C 600 phantom containing contrast rods of various materials is used to assess decomposition accuracy via electron density measurement. Highly accurate electron density maps have become increasingly important in radiation therapy treatment planning for precise dose calculation.…”

Section: D Evaluationmentioning

confidence: 99%

Noise suppression for dual-energy CT via penalized weighted least-square optimization with similarity-based regularization

et al. 2016

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Purpose: Dual-energy CT (DECT) expands applications of CT imaging in its capability to decompose CT images into material images. However, decomposition via direct matrix inversion leads to large noise amplification and limits quantitative use of DECT. Their group has previously developed a noise suppression algorithm via penalized weighted least-square optimization with edge-preservation regularization (PWLS-EPR). In this paper, the authors improve method performance using the same framework of penalized weighted least-square optimization but with similarity-based regularization (PWLS-SBR), which substantially enhances the quality of decomposed images by retaining a more uniform noise power spectrum (NPS). Methods: The design of PWLS-SBR is based on the fact that averaging pixels of similar materials gives a low-noise image. For each pixel, the authors calculate the similarity to other pixels in its neighborhood by comparing CT values. Using an empirical Gaussian model, the authors assign high/low similarity value to one neighboring pixel if its CT value is close/far to the CT value of the pixel of interest. These similarity values are organized in matrix form, such that multiplication of the similarity matrix to the image vector reduces image noise. The similarity matrices are calculated on both high-and low-energy CT images and averaged. In PWLS-SBR, the authors include a regularization term to minimize the L-2 norm of the difference between the images without and with noise suppression via similarity matrix multiplication. By using all pixel information of the initial CT images rather than just those lying on or near edges, PWLS-SBR is superior to the previously developed PWLS-EPR, as supported by comparison studies on phantoms and a head-and-neck patient. Results: On the line-pair slice of the Catphan C 600 phantom, PWLS-SBR outperforms PWLS-EPR and retains spatial resolution of 8 lp/cm, comparable to the original CT images, even at 90% reduction in noise standard deviation (STD). Similar performance on spatial resolution is observed on an anthropomorphic head phantom. In addition, results of PWLS-SBR show substantially improved image quality due to preservation of image NPS. On the Catphan C 600 phantom, NPS using PWLS-SBR has a correlation of 93% with that via direct matrix inversion, while the correlation drops to −52% for PWLS-EPR. Electron density measurement studies indicate high accuracy of PWLS-SBR. On seven different materials, the measured electron densities calculated from the decomposed material images using PWLS-SBR have a root-mean-square error (RMSE) of 1.20%, while the results of PWLS-EPR have a RMSE of 2.21%. In the study on a head-and-neck patient, PWLS-SBR is shown to reduce noise STD by a factor of 3 on material images with image qualities comparable to CT images, whereas fine structures are lost in the PWLS-EPR result. Additionally, PWLS-SBR better preserves low contrast on the tissue image. Conclusions: The authors propose improvements to the regularization term of an optimization frame...

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The noise power spectrum in CT with direct fan beam reconstruction

Cited by 66 publications

References 27 publications

Characterization of statistical prior image constrained compressed sensing. I. Applications to time‐resolved contrast‐enhanced CT

Characterization of statistical prior image constrained compressed sensing. I. Applications to time‐resolved contrast‐enhanced CT

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

Noise suppression for dual-energy CT via penalized weighted least-square optimization with similarity-based regularization

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