Computational Imaging with Limited Photon Budget (original) (raw)
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Computations of the Signal-to-Noise Ratio for Medical X-Ray Imagers
Chinese Journal of Physics, 2014
If the signal in a medical X-ray imaging detector is formed by integrating the scintillation (or electrical) pulses, rather than by counting them, the signal-to-noise ratio is reduced by a factor which depends on the pulse height distribution. Formulas are expanded from Swank's publication to derive the signal-to-noise ratio for any given optical or electrical pulse-size distribution. A new quantity called noise-equivalent absorption is defined which bears a simple relationship to the signal-to-noise ratio of integrated X-ray imaging as the quantum absorption to the signal-to-noise ratio of photon-counting X-ray imaging.
Signal to Noise Ratio in Radiography
Signal to noise ratio in radiography plays an important role in terms of the definition of a discontinuity.The Radiographic SNR value which is a combination of detector SNR and subject SNR related to the subject contrast strongly indicates the detail visibility of an inspection method. In this article, a mathematical model for signal to noise ratio, based on the sensitivity level of the radiographic inspection, will be examined. I. Introduction : The number of photons reaching the radiograph through the Section-A is maximum and will be represented by N(max) and the number of photons reaching the radiograph through the Section-B is minimum and will be represented as N(min), whereas the number of photons falling on the test object will be referred as N(0). The size of the discontinuities will be expressed in terms of " t " and thickness of the test object " T " will be referred as the background signal (noise) level [Figure.1]. The linear attenuation coefficient depending on the specimen material and the radiation energy will be represented by " λ ".
Spatial frequency-dependent signal-to-noise ratio as a generalized measure of image quality
Medical Imaging 2005: Physics of Medical Imaging, 2005
A generalized, objective image quality measure can be defined for X-ray based medical projection imaging: the spatial frequency-dependent signal-to-noise ratio SNR = SNR(u,v). This function includes the three main image quality parameters, i.e. spatial resolution, object contrast, and noise. The quantity is intimately related to the DQE concept, however its focus is not to characterize the detector, but rather the detectability of a certain object embedded into a defined background. So also effects from focus size and radiation scatter can be quantified by this method. The SNR(u,v) is independent of basic linear post-processing steps such as appropriate windowing or spatial filtering. The consideration of the human visual system is beyond the scope of this concept. By means of this quantity, different X-ray systems and setups can be compared with each other and with theoretical calculations. Moreover, X-ray systems (i.e. detector, beam quality, geometry, anti-scatter grid, basic linear postprocessing steps etc.) can be optimized to deliver the best object detectability for a given patient dose. In this paper SNR(u,v) is defined using analytical formulas. Furthermore, we demonstrate how it can be applied with a test phantom to a typical flat panel detector system by a combination of analytical calculations and Monte Carlo simulations. Finally the way this function can be used to optimize an X-ray imaging device is demonstrated.
Noise and signal detection in digital x-ray detectors using the spatial definition of SNR
Society of Photo Optical Instrumentation Engineers Conference Series, 2009
For task specific evaluation of imaging systems it is necessary to obtain detailed descriptions of their noise and deterministic properties. In the past we have developed an experimental and theoretical methodology to estimate the deterministic detector response of a digital x-ray imaging system, also known as the H matrix. In this paper we have developed the experimental methodology for the evaluation of the quantum and electronic noise of digital radiographic detectors using the covariance matrix K. Using the H matrix we calculated the transfer of a simulated coronary artery constriction through an imaging system's detector, and with the covariance matrix we calculated the detectability (or Signal-to-Noise Ratio) and the detection probability. The eigenvalues and eigenvectors of the covariance matrix were presented and the electronic and quantum noise were analyzed. We found that the exposure at which the electronic noise equals the quantum noise at 90 kVp was 0.2 μR. We compared the ideal Hotelling observer with the Fourier definition of the SNR for a toroidal stenosis on a cylindrical vessel. Because of the shift-invariance and cyclo-stationarity assumptions, the Fourier SNR overestimates the performance of imaging systems. This methodology can be used for task specific evaluation and optimization of a digital x-ray imaging system.
Spatial resolution, signal-to-noise and information capacity of linear imaging systems
Optics Express, 2016
A simple model for image formation in linear shift-invariant systems is considered, in which both the detected signal and the noise variance are varying slowly compared to the point-spread function of the system. It is shown that within the constraints of this model, the square of the signal-tonoise ratio is always proportional to the "volume" of the spatial resolution unit. In the case of Poisson statistics, the ratio of these two quantities divided by the incident density of the imaging particles (e.g. photons) represents a dimensionless invariant of the imaging system, which was previously termed the intrinsic imaging quality. The relationship of this invariant to the notion of information capacity of communication and imaging systems, which was previously considered by Shannon, Gabor and others, is investigated. The results are then applied to a simple generic model of quantitative imaging of weakly scattering objects, leading to an estimate of the upper limit for the amount of information about the sample that can be obtained in such experiments. It is shown that this limit depends only on the total number of imaging particles incident on the sample, the average scattering coefficient, the size of the sample and the number of spatial resolution units.
Impact of Additive Noise on System Performance of a Digital X-ray Imaging System
IEEE Transactions on Biomedical Engineering, 2007
The impact of additive noise on the performance of a digital X-ray imaging system was investigated. The X-ray system is uniquely designed for small animal studies with a focal spot of 20 m and an adjustable source-to-object distance for radiography. The noise power spectrum and the detective quantum efficiency of this system were measured. The additive noise increased rapidly when the exposure time exceeded a certain range, since the charge-coupled devices of the detector had no cooling system. The noise power spectrum for the additive noise and the noise of the entire imaging system were studied and compared at different exposure times. The detective quantum efficiency was also measured at different exposure times. It was observed that for exposure times less than 10 s, the detective quantum efficiency ((DQE)(0)) is approximately 0.26, dropping to 0.13 at 4 lp/mm and to 0.026 at 8 lp/mm. However, when the exposure exceeds a certain limit (10 s in this study), the rapidly increased additive noise caused the system to be no longer quantum noise limited, resulting in a decreased detective quantum efficiency and a degraded system performance. For example, at an exposure of 20 s, the DQE(0) is approximately 0.22, dropping to 0.11 at 3 lp/mm and to 0.022 at 8 lp/mm. Index Terms-Additive noise, detective quantum efficiency, digital X-ray imaging, exposure time, noise power spectrum.
Spectral imaging with photon counting detectors has recently attracted a lot of interest in X-ray and CT imaging due to its potential to enable ultra low radiation dose x-ray imaging. However, when radiation exposure level is low, quantum noise may be prohibitively high to hinder applications. Therefore, it is desirable to develop new methods to reduce quantum noise in the acquired data from photon counting detectors. In this paper, we propose a new denoising algorithm to reduce quantum noise in data acquired using an ideal photon counting detector. The proposed method exploits the intrinsic low dimensionality of acquired spectral data to decompose the acquired data in a series of orthonormal spectral bases. The first few spectral bases contain object information while the rest of the bases contain primarily quantum noise. The separation of image content and noise in these orthogonal spatial bases provides a means to reject noise without losing image content. Numerical simulations were conducted to validate and evaluate the proposed noise reduction algorithm. The results demonstrated that the proposed method can effectively reduce quantum noise while maintaining both spatial and spectral fidelity.
International Journal of Engineering Research and Technology (IJERT), 2015
https://www.ijert.org/the-method-of-using-slices-to-estimate-the-noise-power-spectrum-of-a-medical-x-ray-imaging-system https://www.ijert.org/research/the-method-of-using-slices-to-estimate-the-noise-power-spectrum-of-a-medical-x-ray-imaging-system-IJERTV4IS020788.pdf This paper presents Dobbin's method to estimate the noise power spectrum using a screen film system. The one-dimensional spectral estimate was obtained by extracting thick and thin slices from two-dimensional noise power. The slices were made parallel to the primary axis of ROI, but did not include the axis. We measured NPS using one slice, two slices, four slices, eight slices,upper eight slices (a) and eight slices (b) of data in the 128×128 two-dimensional NPS space which were extracted to generate the one-dimensional NPS curves in horizontal and vertical directions and they were compared with Dobbin's method. Very little was found in the NPS shape with regards to the two-dimensional space only and the slice which contained one row and one column was sufficient to study NPS in the two-dimensional space