High Noise Variance Research Articles

Stochastic efficient global optimization with high noise variance and mixed design variables

Stochastic efficient global optimization with high noise variance and mixed design variables

Determination of ingredients in packaged pharmaceutical tablets by energy dispersive X‐ray diffraction and maximum likelihood principal component analysis multivariate curve resolution‐alternating least squares with correlation constraint

AbstractEnergy dispersive X‐ray diffraction (EDXRD) and maximum likelihood principal component analysis multivariate curve resolution‐alternating least squares (MLPCA‐MCR‐ALS) with correlation constraint were used to quantify the composition of packaged pharmaceutical formulations. Recorded EDXRD profiles from unpackaged and packaged samples of ternary mixtures were modelled together in order to recover the concentrations as well as the pure profiles of the constituent compounds. MLPCA was used as a data pretreatment step to MCR‐ALS, accounting for the high noise and nonconstant variance observed in the EDXRD profiles and was shown to improve the resolution accuracy of MCR‐ALS for the data set. Local correlation constraints were applied in the MCR‐ALS procedure in order to model unpackaged and packaged samples simultaneously while accounting for the matrix effect of the packaging materials. The composition of the formulations was estimated with root‐mean‐square error of prediction for each component, including paracetamol, being approximately 2.5 %w/w for unpackaged and packaged samples. Paracetamol concentration was resolved simultaneously for the unpackaged and packaged samples to a greater degree of accuracy than achieved by partial least squares regression (PLSR) when modelling the contexts separately. By modelling the effects of the packaging and incorporating accurate reference information of unpackaged samples into the resolution of packaged samples, the potential of EDXRD and MLPCA‐MCR‐ALS for the identification and quantification of packaged solid‐dosage medicine in nondestructive screening and counterfeit medicine detection has been raised.

Effect of kernel size on Wiener and Gaussian image filtering

In this paper, the effect of the kernel size of Wiener and Gaussian filters on their image restoration qualities has been studied and analyzed. Four sizes of such kernels, namely 3x3, 5x5, 7x7 and 9x9 were simulated. Two different types of noise with zero mean and several variances have been used: Gaussian noise and speckle noise. Several image quality measuring indices have been applied in the computer simulations. In particular, mean absolute error (MAE), mean square error (MSE) and structural similarity (SSIM) index were used. Many images were tested in the simulations; however the results of three of them are shown in this paper. The results show that the Gaussian filter has a superior performance over the Wiener filter for all values of Gaussian and speckle noise variances mainly as it uses the smallest kernel size. To obtain a similar performance in Wiener filtering, a larger kernel size is required which produces much more blur in the output mage. The Wiener filter shows poor performance using the smallest kernel size (3x3) while the Gaussian filter shows the best results in such case. With the Gaussian filter being used, similar results of those obtained with low noise could be obtained in the case of high noise variance but with a higher kernel size.

CT liver tumor segmentation hybrid approach using neutrosophic sets, fast fuzzy c-means and adaptive watershed algorithm.

Liver tumor segmentation from computed tomography (CT) images is a critical and challenging task. Due to the fuzziness in the liver pixel range, the neighboring organs of the liver with the same intensity, high noise and large variance of tumors. The segmentation process is necessary for the detection, identification, and measurement of objects in CT images. We perform an extensive review of the CT liver segmentation literature. Furthermore, in this paper, an improved segmentation approach based on watershed algorithm, neutrosophic sets (NS), and fast fuzzy c-mean clustering algorithm (FFCM) for CT liver tumor segmentation is proposed. To increase the contrast of the liver CT images, the intensity values are adjusted and high frequencies are removed using histogram equalization and median filter approach. It is followed by transforming the CT image to NS domain, which is described using three subsets (percentage of truth T, the percentage of indeterminacy I, and percentage of falsity F). The obtained NS image is enhanced by adaptive threshold and morphological operators to focus on liver parenchyma. The enhanced NS image passed to a watershed algorithm for post-segmentation process and liver parenchyma is extracted using the connected component algorithm. Finally, the liver tumors are segmented from the segmented liver using fast fuzzy c-mean (FFCM). A quantitative analysis is carried out to evaluate segmentation results using six different indices. The results show that the overall accuracy offered by the employed neutrosophic sets is accurate, less time consuming, less sensitive to noise and performs better on non-uniform CT images.

Wavelet transform based novel edge detection algorithms for wideband spectrum sensing in CRNs

The primary task in cognitive radio is to dynamically explore the radio spectrum and reliably detect the co-existing licensed primary transmissions across a wide-band spectrum. This paper focuses on wavelet transform (WT) based wide-band sensing techniques, which identify the edges of the multiple frequency bands simultaneously. Novel edge detection algorithms are proposed based on continuous WT (CWT) and discrete WT (DWT) techniques, applied on wide-band power spectrum. In CWT based spectrum sensing, logarithmic scaling preceded by a thresholding is performed on the CWT coefficients to enhance the small modulus maxima values at the edges, resulting in better detection probability. Since the logarithmic scaling magnifies the spurious edges, the proposed algorithm increases the false alarm probability at high noise variance. To alleviate this problem, DWT based algorithms are proposed, where DWT performs simultaneous denoising and edge detection. To achieve good detection performance at poor SNR scenario, a moving average filtering strategy is adopted at different levels of DWT based algorithms and better performance is achieved even with lower scale value of DWT, thereby reducing the computation time. Comparative studies show that the proposed algorithms outperform the existing WT based edge detection algorithms in the dynamic and frequency selective channels as well.

Review and assessment of latent and sensible heat flux accuracy over the global oceans

For over a decade, several research groups have been developing air-sea heat flux information over the global ocean, including latent (LHF) and sensible (SHF) heat fluxes over the global ocean. This paper aims to provide new insight into the quality and error characteristics of turbulent heat flux estimates at various spatial and temporal scales (from daily upwards). The study is performed within the European Space Agency (ESA) Ocean Heat Flux (OHF) project. One of the main objectives of the OHF project is to meet the recommendations and requirements expressed by various international programs such as the World Research Climate Program (WCRP) and Climate and Ocean Variability, Predictability, and Change (CLIVAR), recognizing the need for better characterization of existing flux errors with respect to the input bulk variables (e.g. surface wind, air and sea surface temperatures, air and surface specific humidities), and to the atmospheric and oceanic conditions (e.g. wind conditions and sea state). The analysis is based on the use of daily averaged LHF and SHF and the associated bulk variables derived from major satellite-based and atmospheric reanalysis products. Inter-comparisons of heat flux products indicate that all of them exhibit similar space and time patterns. However, they also reveal significant differences in magnitude in some specific regions such as the western ocean boundaries during the Northern Hemisphere winter season, and the high southern latitudes. The differences tend to be closely related to large differences in surface wind speed and/or specific air humidity (for LHF) and to air and sea temperature differences (for SHF). Further quality investigations are performed through comprehensive comparisons with daily-averaged LHF and SHF estimated from moorings. The resulting statistics are used to assess the error of each OHF product. Consideration of error correlation between products and observations (e.g., by their assimilation) is also given. This reveals generally high noise variance in all products and a weak signal in common with in situ observations, with some products only slightly better than others. The OHF LHF and SHF products, and their associated error characteristics, are used to compute daily OHF multiproduct-ensemble (OHF/MPE) estimates of LHF and SHF over the ice-free global ocean on a 0.25°×0.25° grid. The accuracy of this heat multiproduct, determined from comparisons with mooring data, is greater than for any individual product. It is used as a reference for the anomaly characterization of each individual OHF product.

Activation volume vs BOLD signal change as measures of fMRI activation – Its impact on GABA – fMRI activation correlation

PurposeTo explore the relative robustness of functional MRI (fMRI) activation volume and blood oxygen level-dependent (BOLD) signal change as fMRI metric, and to study the effect of relative robustness on the correlation between fMRI activation and cortical gamma amino butyric acid (GABA) in healthy controls and patients with multiple sclerosis (MS). MethodsfMRI data were acquired from healthy controls and patients with MS, with the subjects peforming self paced bilateral finger tapping in block design. GABA spectroscopy was performed with voxel placed on the area of maximum activation during fMRI. Activation volume and BOLD signal changes at primary motor cortex (M1), as well as GABA concentration were calculated for each patient. ResultsActivation volume correlated with BOLD signal change in healthy controls, but no such correlation was observed in patients with MS. This difference was likely the result of higher intersubject noise variance in the patient population. GABA concentration correlated with M1 activation volume in patients but not in controls, and did not correlate with any fMRI metric in patients or controls. ConclusionOur data suggest that activation volume is a more robust measure than BOLD signal change in a group with high intersubject noise variance as in patients with MS. Additionally, this study demonstrated difference in correlation behavior between GABA concentration and the 2 fMRI metrics in patients with MS, suggesting that GABA - activation volume correlation is more appropriate measure in the patient group.

On the Capacity of Multiple-Antenna Systems and Parallel Gaussian Channels With Amplitude-Limited Inputs

We propose upper and lower bounds on the capacity of multiple-input multiple-output (MIMO) systems with amplitude-limited inputs. The results are derived by considering an equivalent channel via singular value decomposition, and by enlarging and reducing the corresponding feasible region of the channel input vector, for the upper and lower bounds, respectively. We analytically characterize the asymptotic behavior of the derived bounds for high and low noise levels, and study the gap between them. We also consider parallel Gaussian channels with peak and average power-constrained inputs. For such channels, the capacity-achieving distribution has been reported in the literature to be discrete, which can be computed using numerical optimization techniques. However, there is no closed-form expression and finding the capacity-achieving distribution is computationally tedious. With this motivation, we derive approximate expressions for the capacity at low and high noise variance levels. We illustrate our findings on both MIMO channels and parallel Gaussian channels via several numerical examples.

Estimation Performance for the Bayesian Hierarchical Linear Model

Bayesian hierarchical modelling is a well-established branch of Bayesian inference. In this letter, we derive and study the estimation performance for the Bayesian hierarchical linear model (BHLM). Specifically, we consider a linear model with hierarchical priors for the involved amplitude and noise vectors. We provide closed-form expressions of the Bayesian Cramer-Rao bound (BCRB) for the following settings: (i) an arbitrary prior and hyperprior and (ii) a Gaussian- $\mathcal{Y}$ prior for the amplitudes, while the prior of noise is a Gaussian- $\mathcal{X}$ in both cases. Gaussian- $\mathcal{X}$ means that the conditional prior given the hyperparameter is Gaussian and $\mathcal{X}$ is the hyperprior. For the hierarchical distribution associated with spherical invariant random variables, the BCRB has a compact closed-form expression and enjoys several interesting properties that are discussed. Finally, we provide a theoretical analysis of the statistical efficiency of the linear minimum mean square error (MMSE) estimator in the low- and high-noise variance regimes when the hyperparameters are stochastically dominant.

Complex-valued time-series correlation increases sensitivity in FMRI analysis

PurposeTo develop a linear matrix representation of correlation between complex-valued (CV) time-series in the temporal Fourier frequency domain, and demonstrate its increased sensitivity over correlation between magnitude-only (MO) time-series in functional MRI (fMRI) analysis. Materials and methodsThe standard in fMRI is to discard the phase before the statistical analysis of the data, despite evidence of task related change in the phase time-series. With a real-valued isomorphism representation of Fourier reconstruction, correlation is computed in the temporal frequency domain with CV time-series data, rather than with the standard of MO data. A MATLAB simulation compares the Fisher-z transform of MO and CV correlations for varying degrees of task related magnitude and phase amplitude change in the time-series. The increased sensitivity of the complex-valued Fourier representation of correlation is also demonstrated with experimental human data. Since the correlation description in the temporal frequency domain is represented as a summation of second order temporal frequencies, the correlation is easily divided into experimentally relevant frequency bands for each voxel's temporal frequency spectrum. The MO and CV correlations for the experimental human data are analyzed for four voxels of interest (VOIs) to show the framework with high and low contrast-to-noise ratios in the motor cortex and the supplementary motor cortex. ResultsThe simulation demonstrates the increased strength of CV correlations over MO correlations for low magnitude contrast-to-noise time-series. In the experimental human data, the MO correlation maps are noisier than the CV maps, and it is more difficult to distinguish the motor cortex in the MO correlation maps after spatial processing. ConclusionsIncluding both magnitude and phase in the spatial correlation computations more accurately defines the correlated left and right motor cortices. Sensitivity in correlation analysis is important to preserve the signal of interest in fMRI data sets with high noise variance, and avoid excessive processing induced correlation.

Speckle Noise Reduction for the Enhancement of Retinal Layers in Optical Coherence Tomography Images

Introduction One of the most important pre-processing steps in optical coherence tomography (OCT) is reducing speckle noise, resulting from multiple scattering of tissues, which degrades the quality of OCT images. Materials and Methods The present study focused on speckle noise reduction and edge detection techniques. Statistical filters with different masks and noise variances were applied on OCT and test images. Objective evaluation of both types of images was performed, using various image metrics such as peak signal-to-noise ratio (PSNR), root mean square error, correlation coefficient and elapsed time. For the purpose of recovery, Kuan filter was used as an input for edge enhancement. Also, a spatial filter was applied to improve image quality. Results The obtained results were presented as statistical tables and images. Based on statistical measures and visual quality of OCT images, Enhanced Lee filter (3×3) with a PSNR value of 43.6735 in low noise variance and Kuan filter (3×3) with a PSNR value of 37.2850 in high noise variance showed superior performance over other filters. Conclusion Based on the obtained results, by using speckle reduction filters such as Enhanced Lee and Kuan filters on OCT images, the number of compounded images, required to achieve a given image quality, could be reduced. Moreover, use of Kuan filters for promoting the edges allowed smoothing of speckle regions, while preserving image tissue texture.

Decentralized Activation in Dense Sensor Networks via Global Games

Decentralized activation in wireless sensor networks is investigated for energy-efficient monitoring using the theory of global games. Given a large number of sensors which can operate in either an energy-efficient ldquolow-resolutionrdquo monitoring mode, or a more costly ldquohigh-resolutionrdquo mode, the problem of computing and executing a strategy for mode selection is formulated as a global game with diverse utilities and noise conditions. Each sensor measures its environmental conditions in noise, and determines whether to enter a ldquohigh-resolutionrdquo mode based on its expected contribution and energy cost, which relies on Bayesian estimates of others' observations and actions. We formulate Bayes-Nash equilibrium conditions for which a simple threshold strategy is competitively optimal for each sensor, and propose a scheme for decentralized threshold computation. The threshold level and its equilibrium properties depend on the prior probability distribution of environmental conditions and the observation noise, and we give conditions for equilibrium of the threshold strategy as a function of the prior and observation noise. We also illustrate an interesting phase transition property of the Nash equilibrium for high congestion or low noise variance.

Semi-automatic Segmentation of Liver Tumors from CT Scans Using Bayesian Rule-based 3D Region Growing

Automatic segmentation of liver tumorous regions often fails due to high noise and large variance of tumors. In this work, a semi-automatic algorithm is proposed to segment liver tumors from computed tomography (CT) images. To cope with the variance of tumors, their intensity probability density functions (PDF) are modeled as a bag of Gaussians unlike the previous works where the tumor is modeled as a single Gaussian, and employ a three-dimensional seeded region growing (SRG) method. The bag of Gaussians are initialized at manually selected seeds and updated during growing process iteratively. There are two criteria to be fulfilled for growing: one is the Bayesian decision rule, and the other is a model matching measure. Once the growing is terminated, morphological operations are performed to refine the result. This method, showing promising performance, has been evaluated using ten CT scans of livers with twenty tumors provided by the organizer of the 3D Liver Tumor Segmentation Challenge 2008.

Towards precise classification of cancers based on robust gene functional expression profiles

BackgroundDevelopment of robust and efficient methods for analyzing and interpreting high dimension gene expression profiles continues to be a focus in computational biology. The accumulated experiment evidence supports the assumption that genes express and perform their functions in modular fashions in cells. Therefore, there is an open space for development of the timely and relevant computational algorithms that use robust functional expression profiles towards precise classification of complex human diseases at the modular level.ResultsInspired by the insight that genes act as a module to carry out a highly integrated cellular function, we thus define a low dimension functional expression profile for data reduction. After annotating each individual gene to functional categories defined in a proper gene function classification system such as Gene Ontology applied in this study, we identify those functional categories enriched with differentially expressed genes. For each functional category or functional module, we compute a summary measure (s) for the raw expression values of the annotated genes to capture the overall activity level of the module. In this way, we can treat the gene expressions within a functional module as an integrative data point to replace the multiple values of individual genes. We compare the classification performance of decision trees based on functional expression profiles with the conventional gene expression profiles using four publicly available datasets, which indicates that precise classification of tumour types and improved interpretation can be achieved with the reduced functional expression profiles.ConclusionThis modular approach is demonstrated to be a powerful alternative approach to analyzing high dimension microarray data and is robust to high measurement noise and intrinsic biological variance inherent in microarray data. Furthermore, efficient integration with current biological knowledge has facilitated the interpretation of the underlying molecular mechanisms for complex human diseases at the modular level.

Image sequence stabilisation using fuzzy adaptive Kalman filtering

Image sequence stabilisation based on fuzzy adaptive Kalman filtering of absolute frame displacements is proposed. Two Kalman filters are operated in parallel, one of which is used as a reference filter and is run with a constant high process noise variance to enable smooth and close tracking of global camera displacements. The process noise variance of the stabilisation filter is adaptively varied according to the residual between the stabilisation filter and the reference filter output.

Noise characterization of combined Bellini-type attenuation correction and frequency-distance principle restoration filtering [SPECT

We investigate how successive processing of the projection data with Bellini-type (BT) attenuation correction, frequency distance principle (FDP) restoration filtering, and filtered-backprojection (FBP) reconstruction propagates noise into the reconstructed image. The BT methods, which are Fourier-domain correction techniques, are all exact solutions to the attenuated Radon transform under the constraints of uniform attenuation and a convex object contour. The FDP states that points in the object at a specified distance from the center-of-rotation will contribute predominantly to particular regions of the Fourier transform-series expansion of the sinogram. Using this frequency-distance information, the nonstationary response of the collimator can ideally be deconvolved using an inverse filter. In the presence of noise, however, the FDP filter needs to be regularized in order to control noise amplification caused by the deconvolution. The noise is characterized by calculating the population covariance matrix of the projection data after successive processing with BT attenuation correction and FDP filtering and of the reconstructed image after FBP reconstruction. This is done for a simulated point-source located near the edge of an elliptical, uniformly attenuating medium. In our study, we consider the two implementational combinations of BT correction and FDP filtering that allow for sequential processing of the projection data, which we call mirroring and no mirroring. The results show that the mirroring strategy introduces local positive angular noise correlations in the processed sinogram that are caused by smoothing of the data in the projection angular direction. Furthermore, mirroring highly correlates the noise in opposing projection views. The impact on the image covariance is the presence of positive angular (arc-like) noise correlations. In contrast, the no mirroring strategy yields local positive and negative noise correlations with negative side-lobes in the processed sinogram. Also, no mirroring does not correlate noise in opposing projection views. The result on the image covariance structure is the presence of positive and negative angular correlations with negative side-lobes. It was also noted that the no mirroring scenario produces a much higher noise variance relative to the mirroring implementation of BT attenuation correction and FDP filtering.