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The Signal And The Noise Epub 15


Increasing the spatial resolution in functional Magnetic Resonance Imaging (fMRI) inherently lowers the signal-to-noise ratio (SNR). In order to still detect functionally significant activations in high-resolution images, spatial smoothing of the data is required. However, conventional non-adaptive smoothing comes with a reduced effective resolution, foiling the benefit of the higher acquisition resolution. We show how our recently proposed structural adaptive smoothing procedure for functional MRI data can improve signal detection of high-resolution fMRI experiments regardless of the lower SNR. The procedure is evaluated on human visual and sensory-motor mapping experiments. In these applications, the higher resolution could be fully utilized and high-resolution experiments were outperforming normal resolution experiments by means of both statistical significance and information content.




The Signal And The Noise Epub 15



Background: Differentiating whether an action leads to an outcome by chance or by an underlying statistical regularity that signals environmental change profoundly affects adaptive behavior. Previous studies have shown that anxious individuals may not appropriately differentiate between these situations. This investigation aims to precisely quantify the process deficit in anxious individuals and determine the degree to which these process dysfunctions are specific to anxiety.


Quantitative measurements in the myocardium may be used to detect both focal and diffuse disease processes that result in an elevation of T1 and/or extracellular volume (ECV) fraction. Detection of abnormal myocardial tissue by these methods is affected by both the accuracy and precision. The sensitivity for detecting abnormal elevation of T1 and ECV is limited by the precision of T1 estimates which is a function of the number and timing of measurements along the T1-inversion recovery curve, the signal-to-noise ratio (SNR), the tissue T1, and the method of fitting.


The sensitivity for detecting abnormal elevation of T1 and ECV is limited by the precision of T1 estimates which is a function of the number and timing of measurements along the T1-inversion recovery curve, the signal-to-noise ratio (SNR), the tissue T1, and the method of fitting. Detection of abnormal myocardial tissue by these methods is affected by both the accuracy and precision. In this work, we only consider the random component due to noise which limits precision and not bias errors that affects accuracy. Although absolute accuracy of in-vivo measurements is an important and open subject, these methods have been shown to be highly reproducible [18] in practice despite bias errors.


The sensitivity for detecting abnormal elevation of T1 is limited by the precision of T1 estimates, which in the case of inversion recovery methods is a function of the number and timing of measurements along the T1-recovery curve, the signal-to-noise ratio, tissue T1, method of fitting, and the accuracy of the model. Physiologic fluctuation is not considered. It is proposed to produce a standard deviation (SD) map calibrated in T1 units that represented the standard deviation of the T1 estimate, by transforming the SD of the residual fitting error into the SD of the estimated parameters. Estimate of the T1 parameter error based on fit residuals is derived analytically, and validated by both Monte-Carlo numerical simulation and phantom measurements using repeated trials.


A phase sensitive (PSIR) reconstruction was used [22] to restore the sign and thereby avoid performing a magnitude fit, or performing multiple fits to estimate the zero crossing [9]. In PSIR reconstruction, the real component is used which results in normally distributed noise [23]. The 3-parameter model may be written as:


after having dropped the second order terms in D. D1/2 is comprised of the partial derivatives of the signal Eq (1) relative to the estimated parameters, derived analytically for each inversion time ti as:


where ri are the residuals ϵi after discarding the (p-1) values with lowest magnitude, p = 3 is the number of parameters being fit, and the scale factor 0.6745 is used for noise which is normally distributed. The scale factor is calculated as the median of the absolute value of normally distributed noise with standard deviation equal to 1. Discarding the lowest residuals is necessary to avoid a bias error due to over fitting.


Although the formulation has been developed and validated for PSIR reconstructed images, this formulation may be extended to saturation recovery (SR) methods in cases where the SNR is reasonably high such that the noise distribution is sufficiently normal. It is not readily translated to magnitude IR T1-mapping due to the approximately Rician noise distribution in magnitude signal, particularly near the signal nulls. Furthermore, a frequently used implementation of the MOLLI method originally described [9, 10] that uses the magnitude reconstructed images is based on a multi-fitting approach that perform multiple fits based on successfully incrementing the unknown time of zero-crossing and choosing the value with the best fit. This procedure is essentially estimating a 4-th parameter (the zero-crossing) which degrades the precision for specific values of T1 which have zero-crossings near the inversion times sampled [22].


Lowering injected dose will have an effect on PET image quality. In this article, we aim to investigate this effect in terms of signal-to-noise ratio (SNR) in the liver, contrast-to-noise ratio (CNR) in the lesion, bias and ensemble image noise.


For the evaluation of image quality, five metrics were used 1) SNR in the liver, 2) CNR in the lesion, 3) bias with reference to SUV calculated in the images at the full statistics count level, 4) noise in the image expressed as percentage coefficient of variation (COV) in VOIs including lesion, normal lung and liver, across 10 realizations, and 5) error or reproducibility of the SUVmean and SUVmax in the VOIs including lesion, normal lung and liver, across 10 realizations.


We evaluated image quality with objective metrics including SNR in the liver, CNR in the lesions, bias and noise in the liver, normal lung and lesions, at simulated reduced doses, using 18F-FDG PET data at various count levels from TB patients. The underlying biology of TB is different from that of lung cancer, but for a technical study such as this, the uptake levels in TB lesions will be more representative of early stage lung cancer lesions than those in more advanced lung cancer. This work will lay the foundation to determine the appropriate dose or scan time for a future prospective study with lung cancer patients PET/CT scanning.


Accurate delineation of lesions is a prerequisite for quantification of FDG uptake. Although a large number of approaches have been proposed to segment tumors in PET images including threshold based, gradient based [21], and fuzzy Bayesian based methods [22], accurate tumor segmentation is still a challenging task. This is due to limited spatial resolution and the relatively high noise level in PET images, and this process evidently becomes more challenging with fewer counts (Zaidi and El Naqa, [23]). A simple thresholding method was employed here to segment the solitary lesions in the lung using the full statistics images and the resulting VOIs were copied to the images at the lower count levels. This simple thresholding method may lead to imperfect delineation of the tumor. In addition, the spill-out from the tumor to the surrounding background can lead to lower CNR. However, the inaccurate delineation will not change the behavior of the image metrics since the error will have the same effect at the different count levels, which is partially supported by the result of CNR varying with different threshold (20, 40, 60 and 80 % of SUVmax). Since we work towards low dose PET imaging for those patients at high risk who have indefinite findings with low dose CT screening, VOIs can be delineated on the CT image and copied onto registered PET images.


A consequence of dose or count reduction is a possible bias in SUVmean or SUVmax measurement, and a larger error in the measurement, or degradation of measurement reliability, and an increase of noise in the image, which affects detectability of small lesions. This effect has been studied and a bias has been observed, as well as an increase of noise as COV, and an increase of STE of the SUVmean and SUVmax measurement in different regions of the patient. Several factors influence this including a positive bias in the cold background and negative bias in the hot regions associated with the positivity constraint of the OSEM reconstruction for SUVmean. The SUVmax is easily impacted by count reduction than SUVmean. In Fig. 5, one can observe larger error bars and SUV instability at very low counts.


In the earlier works by Budinger, TF, et al. [26], Hoffman, EJ, et al. [27] and Strother, SC, et al. [28], the relationship between image counts and noise (root-mean-square) had been investigated. These earlier works used a different reconstruction scheme and our findings cannot be compared directly. Notwithstanding this, the statistical noise (COV) in the liver for each subject at the different count level in this study was close to the root-mean square calculated the equation found in the earlier studies up to the count level of 5 million.


ABSTRACT. In this article, the correction of the distorted electrical signal with an adaptive neural fuzzy logic (ANFIS) is discussed due to noise forming at the electrical signal. A sinusoidal signal is widely used both in load supply and in modulation techniques for control and information transport. While the deterioration in a structure of the sinusoidal signal causes energy losses on the power system, it also causes damage to the control signals in the circuit and information transmission signals in telecommunication. Therefore, after considering the structure of the pure reference signal equation, a noise that can occur in the sine structure is included in the reference signal structure. So, an interference signal is formed with the unknown nonlinear process from another noise source for creating the information signal because of an interference signal needs. After an interference signal is generated, the measuring signal is given in the sum of the pure reference signal and the interference signal. For the correction stage of the signals, at inputs of the adaptive fuzzy logic system in the Matlab toolbox, the source signal with noise and the measuring signal values are entered. Then, the experiment is performed via a 3-triangular membership function. When the results are observed, it is seen that the signal which is distorted after the correction operations is very close to the reference signa 350c69d7ab


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