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A new figure of merit for noise in clinical X-ray images illustrated on a mammography application

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Modern image processing and reconstruction procedures require image quality metrics that work without the need for a linear, shift‑invariant system. In collaboration with external partners, Working Group 6.24 (Medical Imaging) is currently developing alternatives to established quality benchmarks. The first building block in this endeavor can now be presented: a non‑parametric statistical quantity for quantifying noise in clinical images, here illustrated based on a series of images recorded on an anthropomorphic mammography phantom.

The new measure τ for noise – the mean threshold level – is based on work carried out by Obuchowicz et al. (2020) [1] and by Bielecka et al. (2020) [2], who suggested a similar approach for MR images. This approach consists in determining the number of picture elements (pixels, abbreviated px) in an image whose gray‑scale value deviates by at least t from all of the next eight neighboring pixels while t is progressively increased from 0 up to a maximum value, and the corresponding number n(t) determined. The new figure of merit τ that we have developed results from the mean value of t weighted with n(t). For noise with a standard deviation σ, τ is proportional to σ. The proportionality factor depends on the noise covariance. This is illustrated in Figure 1 for (simulated) noise with a covariance half width of between 0.1 px and approximately 5 px.

Unlike noise determination in conventional procedures, unstructured background is not required here – which means that noise can be taken directly from a diagnostic image. Currently, the prerequisite for doing so is that the noise covariance decrease relatively quickly as a function of the pixel distance – a requirement that is clearly fulfilled in the case of mammography with a covariance half width of approximately 0.5 px. We are currently working on extending the procedure to include noise with a longer‑range covariance (for example in X‑ray tomography with approximately 1 to 4 px, depending on the image reconstruction method).

Figure 3 shows examples of results from an imaging series performed on an anthropomorphic breast phantom [3] that were recorded at the Referenzzentrum Mammographie SüdWest (Reference Center for Mammography Screening South‑West) in Giessen, Germany, using a Siemens Mammomat Inspiration machine with a tungsten tube and a rhodium filter (W/Rh) at 27 kVp. In addition, simulated microcalcifications were added to regions of interest of the images to be able to compare the new quantity to established image quality estimation methods. They were then assessed using model observers (the channelized Hotelling observer, CHO [4], and the regression detectability index, RDI [5]).

In Figure 3, the values for the detectability d‘ of the two model observers are shown at the top left, and the reciprocal value τ1 of τ is shown at the top right, both as a function of the current‑time product in mAs. This representation makes sense since low noise is usually considered as a sign for superior image quality. The lower part of the image shows the (linear) correlation between d‘ and τ-1. This clearly shows that τ-1 is proportional to an established figure of merit (namely detectability d‘). The value of the proportionality factor depends on the size and contrast of the (simulated) lesions investigated.

The proposed quantity τ is a metric that allows noise to be measured directly from the breast screening images [6].

exponentially correlated noise

Figure 1: Top, from left to right: Exponentially correlated noise, full length at half maximum of the covariance x1/2 from 0.1 px to 5.18 px; bottom: ratio of τ to standard deviation σ of the noise as a function of x1/2

mammographic image

Figure 2: Mammogram of a 3D‑printed breast phantom

3 diagrams detectability

Figure 3: Top left: Detectability d‘ for two model‑based observers (CHO and RDI) as a function of the current‑time product in mAs; top right: τ1 as a function of the current‑time product; bottom: τ-1 as a function of d'


[1]        Obuchowicz, R et al: Magnetic resonance image quality assessment by using non‑maximum suppression and entropy analysis. (2020) Entropy, Vol. 22, No.2, p.220

[2]        Bielecka, M et al: Universal Measure for Medical Image Quality Evaluation Based on Gradient Approach. (2020) Proceedings of the International Conference on Computational Science, p 406-417

[3]        Schopphoven, S et al.: Breast phantoms for 2D digital mammography with realistic anatomical structures and attenuation characteristics based on clinical images using 3D printing. (2019) Physics in Medicine & Biology, Vol. 64, No. 21

[4]        Wunderlich, A et al: Exact Confidence Intervals for Channelized Hotelling Observer Performance in Image Quality Studies. (2015) IEEE Transactions on Medical Imaging, Vol 34, No. 2, p. 453-464

[5]        Anton, M et al: The regression detectability index RDI for mammography images of breast phantoms with calcification‑like objects and anatomical background. (2021) Physics in Medicine & Biology, Vol. 66, No. 22

[6]        Anton, M et al:  A nonparametric measure of noise in x‑ray diagnostic images – Mammography. Submitted to Physics in Medicine & Biology


Opens local program for sending emailM. Anton, Department 6.2, Working Group 6.24


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