Does a Flat Panel Detector Have Enough Bits for Veterinary CT?
What is a good CT scan, and what is good enough?
We will concentrate on stochastic or noise-like errors; i.e. errors that come from the limited number of photons in the signal, electronic noise and the way digital values are derived from the detector signals. In another paper, we will investigate the accuracy of these CT numbers taking into account systematic errors causing image artifacts like shading and distortion of contrast etc. that are not caused by limitations of signal digitization.
This paper is organized as follows:
1. Photon Noise and Image Noise in CT
All x-ray signals have Poisson noise associated with them. The amount depends on the number of x-ray photons making up the signal. Low dose (low photon count) results in grainy images, and high dose (many photons) allows images with lower pixel noise, albeit at the cost of higher patient dose. In order to answer the dose question we have to find out how photon noise in the raw data relates to pixel noise in the image. CT image noise, of course, depends on many factors including the number of projections, the filter kernel, slice thickness, and – most importantly – the attenuation presented by the patient.
By way of example, we establish two relations: (1) how to relate intensity data to photon numbers, and (2) how their stochastic fluctuations propagate to CT image noise.
It turns out that the flat panel used by FIDEX is very close to a quantum device over a large range of signal size. It is essentially a photon counter. The noise associated with the measured intensity signal scales with the square root of the intensity, just as one would expect of a photon counting device. The graph below shows detector signal on the x-axis and noise on the y-axis and obviously it follows the expected square root behavior quite well.
This chart shows that, in the example of FIDEX, one ADC count represents about 1 x-ray photon.
The second relation, how measurement noise generates pixel noise in the CT image, is shown next.
The x-axis shows the approximate number of x-ray photons per sample during data acquisition, and the y-axis is pixel noise in a reconstructed CT image using the FIDEX Standard Algorithm and 0.5 mm slice thickness. To get a diagnostic soft tissue image, one may want to have the image noise below e.g. 8 HU in a 2mm voxel. According to the graph above, this corresponds to approximately 100 photons per sample. (Note that the data was acquired with a large water bottle as absorber).
This sets a limit to the minimum x-ray dose required under the assumption that there is no excess noise. So let’s look at that next.
A perfect detector will not add excess noise to the quantum Poisson noise. In real life, unfortunately, we have to deal with excess noise, and we will consider the following two sources related to bit depth:
If the panel does not have enough bits, then the quantization noise will be too high, generating excess noise. In addition, small signal fluctuation will be added to the same ADC output. As a result, small density variations cannot be seen. Also, if the ADC is too coarse, it is usually associated with lower quality electronic amplifiers, adding excess noise in the analog stage.
2. Quantization noise
Quantization noise is not to be confused with quantum noise. The former is a consequence of digitization while the latter comes from the nature of x-ray photons. One can show that the quantization noise - added to a time-varying signal - is sigma = 1 LSB/√12, where LSB is the least significant bit of the ADC. So the quantization noise is about 0.3 bits. Is that good enough?
It depends on the number of photons this stands for. Rule of thumb: the electronics designer should set the amplifier such that 1 LSB corresponds to about 1 photon. Such a panel is then effectively a photon counter. Imagine a single x-ray photon being absorbed in the detector. It will generate a tiny electrical signal in the amplifier. This signal then moves one bit in the ADC (digitizer). In our case, the ADC quantization will add 0.3 photons rms to the uncertainty of the signal. This is a negligible contribution, so the sensitivity choice taken above is a good one, eliminating electronic quantization noise altogether. The measurements above show that the flat panel used in the FIDEX system has a sensitivity very close to this choice.
With this high sensitivity of about 1 LSB per photon, there is no danger that small signal fluctuations may be merged into a single ADC count. Any signal changes caused by a fluctuation in photon count will also cause corresponding ADC output changes. So quantization noise can be ruled out.
3. Electronic noise
Electronic noise is always a design concern. How much is generated in the amplifiers?
A good unit to measure this is noise-equivalent photons or NEQ. In the case at hand, FIDEX, this happens to be also the number of bits moved by electronic noise. Measurements on several FIDEX systems gave 5.4 counts or NEQ’s for the electronic noise. Is that good enough?
Obviously, electronic noise is substantially more than the quantization noise discussed above, by an order of magnitude. So one has to ask the question, will electronic noise show up in the CT image? Every CT user is familiar with the effect of ‘photon starvation’ in under-dosed images, showing up as directional noise streaks along the rays of maximum attenuation. Therefore, if the electronic noise is of the order of 5.4 photons (NEQ), it will be of the same size as the Poisson noise from 29 photons (5.42). This means we cannot expect to get useful data below about 30 photons per sample, or a factor of 500 down from full scale.
Is this a problem? Would it help if the electronic was designed better, and its noise was zero? The answer is no. A reasonable CT image requires at least 100 photons per data sample, on average. Therefore, the estimated 30 photons coming from electronic noise have negligible effect on the image.
4. Photonic noise and dynamic range
If we take 100 photons as the minimum average signal, and start from 16,000 photons in air (full scale), then we obtain a dynamic range of 16,000/100 = 160. This is indeed not very much. Taking soft tissue with an absorption coefficient of 0.2 cm-1, this allows scanning of patient diameters of up to 25cm. This is about the field of view of a FIDEX machine, and it is rarely exceeded in small animal scanning. Therefore, the available dynamic range of 160 is good enough for soft tissue imaging.
5. Would it be helpful to employ more effective bits?
Yes, it would indeed allow smoother images because one could increase the photon count by a factor of 2 per extra bit. But there are ways to improve without stepping up the dose to the patient. The discussion above assumes air signals to reach full scale, and the dose in the center is just enough for a good CT. It is therefore good practice to employ a bowtie filter absorbing about half of the radiation at the edge of the projection images. This prevents detector saturation without affecting the signal quality in the center of the image where attenuation is usually high. One can argue this adds another effective bit, because it allows doubling the air signal without saturating the panel.
In other words, the question that should be answered is really: would it help to use more dose in the scan? The answer to this is, yes, that would give better and smoother images. And the FIDEX design allows an extra factor of 2 in dose.
In general, however, CT scanners have to be designed to work with the minimum dose required for the application. It is not the design goal to make high-dose, smooth images, but to make diagnostic images with minimal dose.
6. Why do human CT scanners employ more bits in their data acquisition systems?
This is a fair question from radiologists who grew up working with human CT scanners, and who may have a medical CT scanner on hand. Many of these devices use effective 20 bits, made from a 14-bit mantissa and a 6-bit dynamically changing amplifier. The electronic noise floor is typically of the order of 2-3 x-ray photons, a little better but quite comparable to what is achieved in flat panels. However, human CT scanners are capable of increasing the maximum signal way beyond what a flat panel can accept. There are two reasons for this:
An FDCT with 14 bits may not be suitable for a human full body scan, but it is perfectly fine for small animals up to about 100 pounds.
Conclusion: Flat Panel Detectors with 14 bit output are sufficient for small animal CT scanning
The maximum attenuation reachable is about 160 corresponding to 25 cm of water. A well-designed bowtie-filter gives further range. The resulting CT image should be viewed with a 2mm thick slice, and low contrast resolution will be better than 8 HU in a 2x2mm region of interest. The main reason for the capability of 14-bit FDCT systems to compete with 20-bit medical CT scanner data acquisition systems in veterinary applications lies in the smaller size of the patients and the use of smaller detector pixels.
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