Applications of monotonic noise reduction algorithms in fMRI, phase estimation, and contrast enhancement

Abstract

Noise reduction using monotonic fits between extrema has been shown to work well on images, especially those with very low signal‐to‐noise ratios (SNRs). In this article we will explore three applications of monotonic noise reduction in magnetic resonance imaging (MRI). The first application is reducing noise in function MRI (fMRI) studies. Reduced noise allows greater flexibility. For example, it allows the activated regions to be identified using noisier images acquired in less time or fewer cycles of stimulation. Activation maps were calculated from the images after noise reduction had been applied to each image in the series. The parameters used in the noise reduction were optimized so the images produced best matched the average of the entire series. The CNR was improved significantly in the activation maps. The results can be extended to any other fMRI paradigm. The second application was reducing noise in complex data to improve the SNR of the phase in the complex MRI image. The error in the phase was reduced by a factor of three in the simulations shown. In the third application, we introduced a simple contrast‐enhancement method using monotonic noise reduction. To enhance contrast, the coarse features were reduced in size; the smaller size features were increased in size; very small features that are likely to be noise were attenuated. The result is a simple, effective method of improving the contrast of features of a selected size in images with no false features introduced. © 1999 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 10, 177–185, 1999

Best L1 Piecewise Monotonic Data Approximation in Overhead and Underground Medium-Voltage and Low-Voltage Broadband over Power Lines Networks: Theoretical and Practical Transfer Function Determination

“…Concluding the analysis of Section 4, the primary advantage of best L1PMA against least square monotonicity algorithms has been clearly highlighted; in accordance with [60], best L1PMA smooths the data without (i) creating ringing and blurring artifacts around transfer function plots and (ii) inducing round-off error in the modified data [29,59,60,76]. This is due to the fact that, during the calculation of the best L1PMA, the arithmetic operations involved are mainly comparisons so that the median of data of each monotonic section is estimated.…”

“…Brief Presentation of Best L1PMA. During the last 70 years, the monotonic problem has attracted significant interest from many academic fields, such as engineering, health, economics, and statistics, as well as from various applications, including signal restoration, spectroscopy, image processing, and art [29,[58][59][60][61][62][63][64][65]. Among the various proposed monotonic data approximation methods, the application of the best L1PMA, which is theoretically presented and experimentally verified in [27][28][29][30][31][32], successfully copes with problems that are derived from univariate signal restoration.…”

“…(v) Best L1PMA successfully achieves representing either the local extrema or the tail of coupling transfer functions. In contrast with wavelet or spline approximations [72,73], best L1PMA manages to mitigate perturbations (ripples) into the tail of the approximation when a great number of extrema occur [28,59,60,76].…”

Peak Estimation of Univariate Spectraby the Best L1 Piecewise Monotonic Approximation Method

“…In other words, the piecewise monotonic approximation method avoids Gibb's ringing and is able to represent the data at a peak without becoming less accurate away from the peak. In this way, the piecewise monotonicity criterion not only is different from a low-pass filter, which is subject to the Gibbs effect (see, for example, Lanczos [19], Gasquet and Witomski [16]), but also very efficient in denoising signals and images (see, Lu [21] and Weaver [27]).…”