Effect of Noise on MTF Calculations Using Different Phantoms

Purpose: In this work, the effect of noise on the precision in the modulation transfer function (MTF) calculation using different phantoms is investigated. Three different techniques are studied, based on three different phantoms: edge, bar, and star bar. For each technique, theoretical expressions for the standard deviation and the signal to noise ratio (SNR) of the MTF are derived. In addition, Monte Carlo simulations are carried out to study the accuracy and precision of all the three techniques.

Methods: Using the analytic expressions for the MTF calculation, statistical fluctuations of noise in the phantom images are propagated to MTF values. Then, for each frequency the standard deviation and the SNR of the MTF are calculated. Monte Carlo simulations are carried out for each phantom image and for different noise level. Images are artificially generated following a procedure that simulates sampling, blurring, and noise present in a real phantom image and takes into account the attenuation of each phantom. Then, oversampling procedures are applied to these images to obtain presampled MTFs.

Results: In all three techniques the standard deviation of the MTF is proportional to that of the noise in the image. For the edge image, the standard deviation is proportional to the frequency f, whereas for the bar and star bar techniques it is proportional to the square root of f. Regarding the precision, theoretical expressions and simulations results agree that the bar technique shows the best precision for all the frequencies and all the noise levels analyzed in this study. In addition, simulation results show how, for large levels of noise, the edge technique gives rise to large bias errors at high and medium frequencies. Finally, the precision of the star bar technique is similar to that of the bar technique for isotropic systems, but worse for nonisotropic ones.

Conclusion: The uncertainties in the MTF calculation with the edge technique are larger than with the bar technique, and the differences increase with the frequency. On the one hand, the stronger dependency on the frequency shown by the standard deviation of the MTF makes the precision gets worse faster in the edge technique. On the other hand, in the case of the edge and for high levels of noise, differentiation produces line spread functions (LSF) with a poor SNR, increasing erroneously the MTF and worsening accuracy.