Previous research by the author has the theory that histograms of second-order derivatives are capable of determining differences between pixels in MRI images for the purpose of noise reduction without having to refer to ground truth. However, the methodology of the previous research resulted in significant false negatives in determining which pixel is affected by noise. The theory has been revised in this article through the introduction of an additional Laplace curve, leading to comparisons between the histogram profile and two curves instead of just one. The revised theory is that differences between the first curve and the histogram profile and the differences between the second curve and the profile can determine which pixels are to be selected for filtering in order to improve image clarity while minimizing blurring. The revised theory is tested with a modified average filter versus a generic average filter, with PSNR and SSIM for scoring. The results show that for most of the sample MRI images, the theory of pixel selection is more reliable at higher levels of noise but not as reliable at preventing blurring at low levels of noise.

Previous research by the author in the use of histograms of second-order derivatives showed that the differences between pixels in MRI images can be determined without referring to the ground truth for the purpose of noise reduction. Yet, the results of the previous research also showed that the methodologies used could not prevent false positives and negatives. To address this problem, a technique has been developed to involve multiple conditions that utilize the statistics of the histograms and the circumstances of neighbours in the vicinity of a pixel. The confusion matrix for this method shows that the technique has marginal but consistent improvement across the noise levels that are tested, compared to prior methods