Noise
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CT noisethe manifestation in computed tomography CT images of random fluctuations in the measurements due to quantum noise in the detected X rays and other noise sources such as electronic noise. CT noise has a variety of unique properties which result from the application of the CT reconstruction algorithm to the errors in the original signal measurements. Properties include:
1) A noise spike in a single measurement in a single view is reconstructed as a bright streak with negative side lobes. Thus a single noise spike has an effect which propagates through the entire image.
2) When the projection measurements are uniformly affected by additive noise, the magnitude of the noise in the CT image is directly proportional to the magnitude of the input measurement noise. Thus any process, such as increased X-ray dose, which decreases input measurement noise will proportionately decrease the image noise. For example, the quantum noise in CT images is inversely related to the square root of the dose.
3) Because each projection measurement affects the entire image, the final image noise exhibits a long range spatial correlation. In fact the noise exhibits negative long range correlation such that a positive noise spike in one projection data point will tend to decrease the values at image points distant from the corresponding ray. This gives CT noise a "wormy" or streaky appearance (
).
4) When the projection data has additive white noise, the noise in the CT image is not white. The CT image has much more noise at high frequencies than at low frequencies. This is a direct result of the oversampling of the low spatial frequencies.
5) When attempts are made to increase the spatial resolution of a CT image, the image noise increases much faster than it does in projection imaging. For example, doubling of the spatial resolution in two dimensions in a projection image (or any image with white noise) increases the noise by a factor of 2. However, in CT the increase in noise level is a factor of 2.8 (2Ö2 ). On the other hand, the long range negative correlation of the noise maintains the detectability of large area low contrast objects. The detectability of such large objects is independent of the spatial resolution used in the imager, and only depends on the X-ray dose efficiency of the detection process. In addition, retrospective smoothing or filtering fully recovers the noise increase.
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1) A noise spike in a single measurement in a single view is reconstructed as a bright streak with negative side lobes. Thus a single noise spike has an effect which propagates through the entire image.
2) When the projection measurements are uniformly affected by additive noise, the magnitude of the noise in the CT image is directly proportional to the magnitude of the input measurement noise. Thus any process, such as increased X-ray dose, which decreases input measurement noise will proportionately decrease the image noise. For example, the quantum noise in CT images is inversely related to the square root of the dose.
3) Because each projection measurement affects the entire image, the final image noise exhibits a long range spatial correlation. In fact the noise exhibits negative long range correlation such that a positive noise spike in one projection data point will tend to decrease the values at image points distant from the corresponding ray. This gives CT noise a "wormy" or streaky appearance (
).4) When the projection data has additive white noise, the noise in the CT image is not white. The CT image has much more noise at high frequencies than at low frequencies. This is a direct result of the oversampling of the low spatial frequencies.
5) When attempts are made to increase the spatial resolution of a CT image, the image noise increases much faster than it does in projection imaging. For example, doubling of the spatial resolution in two dimensions in a projection image (or any image with white noise) increases the noise by a factor of 2. However, in CT the increase in noise level is a factor of 2.8 (2Ö2 ). On the other hand, the long range negative correlation of the noise maintains the detectability of large area low contrast objects. The detectability of such large objects is independent of the spatial resolution used in the imager, and only depends on the X-ray dose efficiency of the detection process. In addition, retrospective smoothing or filtering fully recovers the noise increase.
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