The Contrast to Noise Ratio (CNR) in a medical image is a measure of the contrast between the tissue of interest and the background (i.e. the neighboring tissue). The Signal to Noise Ratio (SNR) is a measure of the image signal in a given region to the background. The ability to visualize objects in a noisy background is dependent on the size of the objects and the contrast of the objects. In this article we will cover the basics of Contrast to Noise for you as a Radiographer / Radiologic Technologist.
Signal to Noise Ratio (SNR) and Contrast to Noise Ratio (CNR)
In all diagnostic imaging there is a trade-off between noise and image acquisition parameters. In x-ray and CT imaging the trade-off is the radiation dose the patient receives, while in MRI it is scan time.
Therefore, the optimal images will always have a reasonable amount of noise (otherwise the scan is acquired at a radiation dose that is too high or in the case of MR the scan time is too long).
A very common clinical task in x-ray or CT is to determine if there is something undesirable in the image such as a tumor or another type of lesion. In this case we call the tumor the image signal of interest and the task is differentiating it from the background tissue.
In this section we will discuss the concepts of Signal to Noise Ratio (SNR) and Contrast to Noise Ratio (CNR). These measures help us understand how well the diagnostic task can be performed, even when noise is present in the images.
Quantum Noise (a.k.a. Quantum Mottle)
In x-ray and CT images the source of noise in the images is referred to as quantum noise or quantum mottle. This is due to the photon counting statistics, i.e. when more photons are counted in the detector the images will be less noisy. However, in order to get more photons counted in the detector the x-ray radiation dose will be higher.
Therefore, for each specific imaging task it is important to select the appropriate radiation dose such that the noise is not too high so that the signal of interest can be visualized above background tissue.
Here is an example of an image with increasing levels of quantum noise. In the upper left there are no noise fluctuations and then higher levels of noise are present until the lower right which has the highest level of quantum noise.
From this small example you can see that even at the higher noise cases it is still possible to differentiate many things within the image. If the clinical task was to tell if there are two eyes a nose and a mouth then even the noisiest image would be acceptable for this task.
However, if the task is to draw a border of the outline of the head including the hair then there is too much noise in the high noise images.
This is just a toy example and obviously not medical images but the point here is that depending on the clinical task the acceptable noise in the images can be significantly different.
Rad Take-home Point: Image noise increases in x-ray and CT imaging when the radiation dose is lowered. The required radiation dose is strongly dependent on the clinical task for the given exam.
If we have different disks on the image, ability to see them depends on how big and bright they are. In this example we have disks with three different signal levels that are low, med and higher contrast levels.
Depending on the clinical task the signal in the image will have a different level above the background tissue.
Measuring SNR and CNR
The signal to noise ratio (SNR) is simply the average image signal in a given region divided by the noise around that region. This can be a useful first measurement but the more important quantity typically is the contrast to noise ratio (CNR), which is simply the ratio of the contrast between the signal in a given region and the background.
SNR and CNR are calculated with following formulas:
So how do we make these measurements in practice. We typically place what is called a Region of Interest (ROI) on the image. This ROI will select all the image pixels inside of the selected region.
Then the image viewing software will typically report at least a couple key measurements inside of each ROI. The average image signal in that ROI and the standard deviation of noise in that ROI.
With the capability to measure both the signal level and the noise level in given ROIs we can calculate the SNR and CNR for a given acquisition.
We give a small example here to demonstrate these concepts.
For instance, if have an average signal strength of 150 and standard deviation of the noise of 10 what will the SNR be?
For instance, if we then measure the average in the background ROI around the signal ROI to be 100 what is the CNR?
We can see that the CNR is different from the SNR and that the CNR is very dependent on the local contrast. As the CNR is increased the objects will be more easily visualized with respect to the background.
Rad Take-home Point: SNR (Signal to Noise Ratio) and CNR (Contrast to Noise Ratio) can be calculated based on measurements within Regions of Interest (ROIs) in medical images.
Perceived Image Quality (Rose Model)
Since we are spending time to make measurements in the image we want to be aware that these are important quantities for our ability to perform diagnostic tasks.
Here we have sample circular signals of different size that are placed in a uniform background. While this is more ideal than a typical medical image it can give us a good idea of the effect of quantum noise on the image.
In this figure we show the effect of modifying the contrast and the noise in the images.
Examples of mechanisms to increase contrast in an x-ray image include: increasing the rate and/or volume of iodine contrast injection or lowering the kVp of the acquisition.
On the other hand, the noise will be increased in an x-ray image when the radiation dose is reduced.
In this figure as we move from left to right the noise level is increased by a factor of 4 so it becomes much more obvious in the images.
In the figure as we move from top to bottom the contrast level is decreased by a factor of 3 which makes it much more difficult to visualize the signal regions from the background.
This shows the value of the CNR measurements as it correlates with the ability to differentiate the signals from the background.
We also note that the smaller signal region is the first to ‘disappear’ and become difficult to identify from the background as the CNR decreases. For instance, in the case of CNR=0.5 it becomes difficult to visualize. Then after that even the medium object becomes difficult to visualize when CNR=0.25.
In this figure the same display settings are kept constant for all images, which is why the images with the same CNR may look slightly different as the contrast level is changing in the images.
Object size and Contrast
As we noted above at the same contrast level we lose the ability visualize the small objects before the large objects.
In the late 1940s this phenomena was described for simple simulated objects in the Rose Model (A. Rose, “The sensitivity performance of the human eye on an absolute scale.”, J. Opt. Soc. Am. 38, (1948) ).
where C is Contrast, A is the area of the lesion and N is the number of photons. While this early model was very simplified and does not identify a specific clinical task, it is still useful to have a basic idea of how these parameters are related.
In this figure we modify the contrast of the objects based on their size. As the area becomes smaller the contrast is increased. In this manner the objects have similar visibility or detectability as the noise is increased. This is different from the figure above with different levels of contrast and noise where the largest object was the only one visible as the noise level was increased.
In clinical practice the situation is more complicated than this as there is background anatomy, and in x-ray imaging there is overlying anatomical clutter in the projections as well.
Rad Take-home Points:
- The CNR (Contrast to Noise Ratio) can be calculated based on measurements within Regions of Interest (ROIs) in medical images.
- For simple objects in a uniform background the ability to identify the objects is directly dependent on the contrast and the sqrt of the area.