SNR of MTF calculations in non wide sense stationary systems

Abstract

Noise in phantom images is propagated to MTF calculated values, increasing their uncertainty. In this work, the phantom that maximizes the signal to noise ratio (SNR) of the MTF is determined as a function of spatial frequency and noise in the images. New analytic expressions for the SNRs of the MTF are derived, and formerly published ones are modified to take into account that real noise is not wide sense stationary (WSS). Five phantoms are used: slit, wire, edge, bar and star-bar. The SNRs are inversely proportional to the frequency in the slit, wire and edge methods. For the phantoms based in periodic pattern, the SNRs are inversely proportional to the squared root of frequency. In the slit and wire methods, an oscillating factor is also present. The loss of the WSS of noise determines the contribution of quantum noise to the SNR. This contribution is negligible in the slit case and remains unaltered in the wire case. The edge, bar and star-bar represent intermediate cases. Finally, ratios of the SNRs between the different methods are provided. These ratios quantify the relative uncertainty of two methods as a function of frequency, noise and the physical dimensions of the phantoms. In this way, these ratios can be used to determine which method produces the optimal SNR in any situation.

Performance of a new star‐bar phantom designed for MTF calculations in x‐ray imaging systems

“…The uncertainty in the MTF determination with star‐bar phantoms has been previously studied 21,22 . In these works, theoretical expressions were derived for the MTF standard deviation for several phantoms.…”

“…The uncertainty in the MTF determination with star-bar phantoms has been previously studied. 21,22 In these works, theoretical expressions were derived for the MTF standard deviation for several phantoms. In, 22 the squared-SNR of the MTF was expressed as a function of frequency f for five different phantoms as…”

“…It is shown that the standard deviation (SD) of the MTF is proportional to the frequency. [20][21][22] Also, it has been shown that the information of intermediate and high frequencies is encapsulated in a small area of the edge image. 23 A theoretical method for MTF calculations using star-bar phantoms has been presented in Ref.…”

“…[23] Some aspects of the theory, like using higher order harmonics or determining its uncertainties have also been developed in Ref. [21,22,24] One important result states that the SD of the MTF determination is proportional to the square root of the frequency, 21,22 a better behavior than that of the edge method.…”

“…However, the precision of the MTF calculated by the edge method is not constant and has a strong dependency with frequency. It is shown that the standard deviation (SD) of the MTF is proportional to the frequency 20–22 . Also, it has been shown that the information of intermediate and high frequencies is encapsulated in a small area of the edge image 23 …”