Intersection Of Confidence Intervals Research Articles

Optimization assisted autoregressive technique with deep convolution neural network-based entropy filter for image demosaicing

ABSTRACT This paper presents an image demosaicing based on an optimization-driven deep learning model, namely the Autoregressive Water Wave Optimization algorithm (Autoregressive-WWO). The proposed method is devised by assimilating the Wave Optimization algorithm (WWO), and the Conditional autoregressive value at risk (CAViaR) model. Here, the input images are subjected to Autoregressive WWO-based local polynomial approximation and intersection of confidence intervals (LPA-ICI) filter, and Deep Convolution neural network (Deep CNN) in a concurrent manner. The filter coefficients are obtained from the proposed Autoregressive WWO-based LPA-ICI filter and the residual image is obtained from Deep CNN. In order to create the demosaiced image, these two outputs are combined using an entropy measure. The proposed method offered superior performance with the highest Peak signal to noise ratio (PSNR) of 40.049dB, the highest Second derivative measure of enhancement (SDME) of 50.168dB, and highest Structural Index Similarity (SSIM) of 0.9056.

Enhancement of video demosaicing techniques using optimization algorithm

SummaryDemosaicing and denoising are the most significant steps in the imaging process for both images and videos. The correlation noise corrupts the image quality, such that an accurate interpretation of the image is avoided. Thus, demosaicing is utilized to restructure the full‐color image from imperfect color samples. In this article, cat shuffled shepherd optimization‐based local polynomial approximation and intersection of confidence intervals (Cat SSO‐based LPA‐ICI) approach is developed for video demosaicing. The LPA‐ICI model is employed for frame demosaicing in which the second‐order polynomial interpolation filter coefficients are produced using the devised optimization algorithm, named cat SSO technique. Similarly, generative adversarial network classifier is also applied for frame demosaicing. In addition, initialization and flow estimation is performed for the demosaicing process. Besides, spatio temporal demosaicing model is utilized in order to get a noise‐free sequence. However, the developed cat SSO technique is newly devised by the incorporation of the shuffled shepherd optimization algorithm and cat swarm optimization technique. The created video demosaicing model outperformed with peak signal‐to‐noise ratio, root mean square error, and second derivative‐like measure of enhancement values of 56.85 dB, 0.46, and 60.62, respectively.

Anisotropic Denoising of 3D Point Clouds by Aggregation of Multiple Surface-Adaptive Estimates.

3D point clouds commonly contain positional errors which can be regarded as noise. We propose a point cloud denoising algorithm based on aggregation of multiple anisotropic estimates computed on local coordinate systems. These local estimates are adaptive to the shape of the surface underlying the point cloud, leveraging an extension of the Local Polynomial Approximation (LPA) - Intersection of Confidence Intervals (ICI) technique to 3D point clouds. The adaptivity due to LPA-ICI is further strengthened by the dense aggregation with data-driven weights. Experimental results demonstrate state-of-the-art restoration quality of both sharp features and smooth areas.

Phase unwrapping based on accumulation of residual maps with local denoising

Phase unwrapping aims to reconstruct the absolute phase from its values mod 2π, which is a key problem in many non-contact optical metrologies and is still a challenging issue in the presence of noise. We present a robust phase unwrapping method with two steps based on local denoising and the accumulation of residual map (ARM). In the first step, based on the local polynomial approximations and intersection of confidence intervals, we adopt a sine–cosine filtering and iteration algorithm to denoise the wrapped phase, which uses the periodicity of the trigonometric function to avoid the influence of phase jumps effectively. In the second step, the denoised wrapped phase is unwrapped by the improved ARMs method, in which we modify the edge regular term to avoid over-fitting and maintain edge information. The algorithm is tested with a set of numerical simulations under various noise levels, and the experimental results confirm its effectiveness and robustness.

Gravitational-Wave Burst Signals Denoising Based on the Adaptive Modification of the Intersection of Confidence Intervals Rule.

Gravitational-wave data (discovered first in 2015 by the Advanced LIGO interferometers and awarded by the Nobel Prize in 2017) are characterized by non-Gaussian and non-stationary noise. The ever-increasing amount of acquired data requires the development of efficient denoising algorithms that will enable the detection of gravitational-wave events embedded in low signal-to-noise-ratio (SNR) environments. In this paper, an algorithm based on the local polynomial approximation (LPA) combined with the relative intersection of confidence intervals (RICI) rule for the filter support selection is proposed to denoise the gravitational-wave burst signals from core collapse supernovae. The LPA-RICI denoising method’s performance is tested on three different burst signals, numerically generated and injected into the real-life noise data collected by the Advanced LIGO detector. The analysis of the experimental results obtained by several case studies (conducted at different signal source distances corresponding to the different SNR values) indicates that the LPA-RICI method efficiently removes the noise and simultaneously preserves the morphology of the gravitational-wave burst signals. The technique offers reliable denoising performance even at the very low SNR values. Moreover, the analysis shows that the LPA-RICI method outperforms the approach combining LPA and the original intersection of confidence intervals (ICI) rule, total-variation (TV) based method, the method based on the neighboring thresholding in the short-time Fourier transform (STFT) domain, and three wavelet-based denoising techniques by increasing the improvement in the SNR by up to 118.94% and the peak SNR by up to 138.52%, as well as by reducing the root mean squared error by up to 64.59%, the mean absolute error by up to 55.60%, and the maximum absolute error by up to 84.79%.

A novel approach to extracting useful information from noisy TFDs using 2D local entropy measures

The paper proposes a novel approach for extraction of useful information and blind source separation of signal components from noisy data in the time-frequency domain. The method is based on the local Rényi entropy calculated inside adaptive, data-driven 2D regions, the sizes of which are calculated utilizing the improved, relative intersection of confidence intervals (RICI) algorithm. One of the advantages of the proposed technique is that it does not require any prior knowledge on the signal, its components, or noise, but rather the processing is performed on the noisy signal mixtures. Also, it is shown that the method is robust to the selection of time-frequency distributions (TFDs). It has been tested for different signal-to-noise-ratios (SNRs), both for synthetic and real-life data. When compared to fixed TFD thresholding, adaptive TFD thresholding based on RICI rule and the 1D entropy-based approach, the proposed adaptive method significantly increases classification accuracy (by up to 11.53%) and F1 score (by up to 7.91%). Hence, this adaptive, data-driven, entropy-based technique is an efficient tool for extracting useful information from noisy data in the time-frequency domain.

Improved power system state estimator with preprocessing based on the modified intersection of confidence intervals

Abstract The paper proposes a power system state estimator upgraded by the improved relative intersection of confidence intervals (RICI) algorithm combined with the local polynomial approximation (LPA). In the proposed approach, a novel LPA-RICI denoising technique is utilized to preprocess the input measurements. The accuracy of the adaptive, data-driven LPA-RICI based state estimator was tested on the IEEE test systems with 14 and 30 buses, as well as on a model of the real-life Croatian transmission power system. Due to its adaptivity to high transitions in measurement series achieved by varying filter support size, the LPA-RICI based state estimator enhanced the estimation accuracy for all tested power systems, and at the same time reduced the number of iterations required for the estimator to converge when compared to the classical weighted least squares (WLS) based estimator. Namely, improvement when using the proposed preprocessor was obtained in estimation of the input voltage magnitudes, active and reactive power flows and injections for the Croatian transmission power system by up to 29.3% and 19.4% in terms of the reduction of the mean squared error (MSE) and mean absolute error (MAE), respectively. Furthermore, the LPA-RICI based estimator resulted in an overall estimation quality enhancement for the Croatian transmission power system by up to 13.3%, 12.3%, and 3.7%, in terms of the objective function, variance of the estimated states, and average time for the state estimator to converge, respectively.

An active contour model for medical image segmentation using a quaternion framework

This paper presents a new method for segmenting medical images is based on Hamiltonian quaternions and the associative algebra, method of the active contour model and LPA-ICI (local polynomial approximation - the intersection of confidence intervals) anisotropic gradient. Since for segmentation tasks, the image is usually converted to grayscale, this leads to the loss of important information about color, saturation, and other important information associated color. To solve this problem, we use the quaternion framework to represent a color image to consider all three channels simultaneously when segmenting the RGB image. As a method of noise reduction, adaptive filtering based on local polynomial estimates using the ICI rule is used. The presented new approach allows obtaining clearer and more detailed boundaries of objects of interest. The experiments performed on real medical images (Z-line detection) show that our segmentation method of more efficient compared with the current state-of-art methods.

Adaptive instantaneous frequency estimation based on time-frequency distributions with derivative approximation

Abstract A new method for nonparametric and adaptive instantaneous frequency (IF) estimation of monocomponent signals based on time-frequency distributions (TFDs) is presented. This method uses an estimate of the IF second-order derivative to approximate the width of the TFD observation window associated with the estimation least mean squared error (MSE), which was previously derived in a closed-form expression. The derivative estimate is obtained in two steps. First, a preliminary TFD is computed and its local maxima are used as a rough estimate of the IF trajectory. Thence, the continuous wavelet transform (CWT) is introduced for calculations of high-order derivatives. The proposed method is evaluated and compared with state-of-the-art algorithms based on the intersection of confidence intervals (ICI) rule. Numerical results demonstrate that the proposed method achieves a significant improvement in estimation accuracy.

Optimised halftoning and inverse halftoning of dermoscopic images for supporting teledermoscopy system

Telemedicine systems require reliable, small size, and secure transmission. In teledermoscopy, the transmission of the traditional large size dermoscopic images leads to heavy consumption of storage space and bandwidth congestion, which impairs the efficient use of the transmission channel bandwidth. Furthermore, halftoning and inverse halftoning have a great practical impact in the reduction of the images' size. For teledermoscopy, the present work optimises the error filter during the error diffusion process to generate the halftone dermoscopic images with small size. The proposed inverse halftone optimises two parameters during the integration between the regularised inverse filter and the DLPA-ICI (directional local polynomial approximation and the intersection of confidence intervals) estimator's kernel. The optimised kernel parameter determines the best window size of the kernel in the restored image estimation. The experimental results included comparative studies in terms of several image quality metrics and the average size reduction in percentage when using the genetic algorithm for optimisation with Jarvis error diffusion for halftone images generation. The achieved average size reduction is 92.15% using the proposed method compared to the average dermoscopic images' size in the test set on 900 images showing the superiority of the proposed method.

The quaternion-based anisotropic gradient for the color images

Image gradient, as a preprocessing step is an essential tool in image processing in many research areas such as edge detection, segmentation, smoothing, inpainting, etc. In the present paper, we develop a new gradient by integrated the quaternion framework with LPA-ICI (local polynomial approximation – the intersection of confidence intervals) based on anisotropic gradient concepts for the color image processing applications. Computer simulations on the Berkeley Segmentation Dataset show that the new quaternion anisotropic gradient exhibits fewer color artifacts compared to state-of-the-art techniques including well-knowledge gradient operators.

An adaptive method based on the improved LPA-ICI algorithm for MRI enhancement

ABSTRACTVarious diseases are diagnosed using medical imaging used for analysing internal anatomical structures. However, medical images are susceptible to noise introduced in both acquisition and transmission processes. We propose an adaptive data-driven image denoising algorithm based on an improvement of the intersection of confidence intervals (ICI), called relative ICI (RICI) algorithm. The 2D mask of the adaptive size and shape is calculated for each image pixel independently, and utilized in the design of the 2D local polynomial approximation (LPA) filters. Denoising performances, in terms of the PSNR, are compared to the original ICI-based method, as well as to the fixed sized filtering. The proposed adaptive RICI-based denoising outperformed the original ICI-based method by up to 1.32 dB, and the fixed size filtering by up to 6.48 dB. Furthermore, since the denoising of each image pixel is done locally and independently, the method is easy to parallelize.

Adaptive state estimator with intersection of confidence intervals based preprocessing

The paper presents an effective solution for improving power system state estimation performance by applying the intersection of confidence intervals (ICI) algorithm, a state-of-the-art adaptive signal processing technique used in signal denoising. Since many power utilities worldwide still run state estimators based on the weighed least squares (WLS) algorithm using supervisory control and data acquisition (SCADA) measurements, the ICI algorithm is added to pre-process SCADA measurements without changing the structure of the WLS algorithm. Due to its adaptive window size and high sensitivity to noise in the input measurement series, the proposed ICI-based solution results in an enhancement of the state estimator output and overall performance when compared to the original algorithm. As test beds, the IEEE systems with 30 and 118 buses were used, while as an example of the real power system, the complete mathematical model of the Croatian transmission power system was simulated. Several case studies indicate that the ICI-based state estimator reduces the input measurements mean squared error by up to 30.8%, the mean absolute error by up to 20.8%, and the maximum estimation error by up to 22.6%. Furthermore, this also led to an enhanced final output of the state estimator for all tested systems in view of the state estimation accuracy and convergence.

Local polynomial approximation and intersection of confidence intervals for removing noise of lightning electric field measurements

Las mediciones de campo eléctrico producido por rayos (LEF) son señales aperiódicas caracterizadas por ruido inherente de diferentes fuentes, es decir, no es posible registrar una señal libre de ruido. En la última década, se ha logrado filtrar mediciones de LEF utilizando algunas representaciones tiempo-frecuencia tales como la transformación de Fourier de corto tiempo (STFT), la transformación wavelet (WT) y la transformación de Fourier fraccionaria (FRFT) sin resultados definitivos. En este trabajo, se propone un proceso de eliminación de ruido aplicado a mediciones de LEF usando la aproximación polinomial local (LPA). La selección del tamaño de la ventana se realiza combinando la LPA con el algoritmo de intersección de intervalos de confianza (ICI). Además, un criterio de validación cruzada se utiliza para seleccionar el valor óptimo del umbral en el método de reducción de ruido LPA-ICI. Se muestra que para diferentes valores de relación señal-a-ruido (SNR), el método propuesto reduce significativamente el ruido presente en las señales registradas. Finalmente, se realiza una discusión sobre las señales procesadas en términos de algunas características temporales del campo eléctrico.

Denoising of X-ray Images Using the Adaptive Algorithm Based on the LPA-RICI Algorithm

Diagnostics and treatments of numerous diseases are highly dependent on the quality of captured medical images. However, noise (during both acquisition and transmission) is one of the main factors that reduce their quality. This paper proposes an adaptive image denoising algorithm applied to enhance X-ray images. The algorithm is based on the modification of the intersection of confidence intervals (ICI) rule, called relative intersection of confidence intervals (RICI) rule. For each image pixel apart, a 2D mask of adaptive size and shape is calculated and used in designing the 2D local polynomial approximation (LPA) filters for noise removal. One of the advantages of the proposed method is the fact that the estimation of the noise free pixel is performed independently for each image pixel and thus, the method is applicable for easy parallelization in order to improve its computational efficiency. The proposed method was compared to the Gaussian smoothing filters, total variation denoising and fixed size median filtering and was shown to outperform them both visually and in terms of the peak signal-to-noise ratio (PSNR) by up to 7.99 dB.

A Fast Signal Denoising Algorithm Based on the LPA-ICI Method for Real-Time Applications

We propose a new algorithm for denoising of additive white Gaussian noise-corrupted signals, based on the intersection of confidence intervals (ICI) algorithm, called the fast intersection of confidence intervals (FICI) algorithm. The proposed approach combines the FICI algorithm, used for the adaptive filter support size selection, with the local polynomial approximation (LPA) method, used as a filter design tool. The LPA-FICI method, when compared to the existing ICI-based denoising method, reduces the computational complexity by up to N times, where N is the number of signal samples, resulting in significantly faster algorithm execution time, while maintaining the estimation accuracy close to the one achieved using the original ICI-based method. Furthermore, the proposed modifications allow the use of the LPA-FICI method in real-time signal processing. In conducted simulations, we have confirmed advantages of the proposed method on two commonly used benchmark signals corrupted with various noise strengths.

Optimum short-time polynomial regression for signal analysis

We propose a short-time polynomial regression (STPR) for time-varying signal analysis. The advantage of using polynomials is that the notion of a spectrum is not needed and the signals can be analyzed in the time domain over short durations. In the presence of noise, such modeling becomes important, because the polynomial approximation performs smoothing leading to noise suppression. The problem of optimal smoothing depends on the duration over which a fixed-order polynomial regression is performed. Considering the STPR of a noisy signal, we derive the optimal smoothing window by minimizing the mean-square error (MSE). For a fixed polynomial order, the smoothing window duration depends on the rate of signal variation, which, in turn, depends on its derivatives. Since the derivatives are not available a priori, exact optimization is not feasible. However, approximate optimization can be achieved using only the variance expressions and the intersection-of-confidence-intervals (ICI) technique. The ICI technique is based on a consistency measure across confidence intervals corresponding to different window lengths. An approximate asymptotic analysis to determine the optimal confidence interval width shows that the asymptotic expressions are the same irrespective of whether one starts with a uniform sampling grid or a nonuniform one. Simulation results on sinusoids, chirps, and electrocardiogram (ECG) signals, and comparisons with standard wavelet denoising techniques, show that the proposed method is robust particularly in the low signal-to-noise ratio regime.

Multicomponent noisy signal adaptive instantaneous frequency estimation using components time support information

This study proposes an adaptive method for components instantaneous frequency (IF) estimation of noisy non-stationary multicomponent signals, combined with the components time-support estimation method based on the short-time Rényi entropy (STRE). Components localisation and separation are done using a double-direction component tracking and extraction method presented here, while the IF estimation is done using the adaptive algorithms based on the intersection of confidence intervals (ICI) rule and the relative intersection of confidence intervals (RICI) rule. The results obtained using the ICI and RICI rules are compared for various window types, signal-to-noise ratios and time–frequency distributions, both with and without using the information on components time support. Most of the errors in IF estimation using the ICI and RICI-based methods are caused by imprecise components time-support estimation. The proposed methods combined with the STRE have achieved a significant accuracy improvement in terms of the mean absolute error and the mean squared error, reducing them by up to 73 and 93%, respectively. The method has been applied to real-life signals and proven to be an efficient tool for IF estimation of noisy non-stationary multicomponent signals.

Adaptive covariance estimation of non-stationary processes and its application to infer dynamic connectivity from fMRI.

Time-varying covariance is an important metric to measure the statistical dependence between non-stationary biological processes. Time-varying covariance is conventionally estimated from short-time data segments within a window having a certain bandwidth, but it is difficult to choose an appropriate bandwidth to estimate covariance with different degrees of non-stationarity. This paper introduces a local polynomial regression (LPR) method to estimate time-varying covariance and performs an asymptotic analysis of the LPR covariance estimator to show that both the estimation bias and variance are functions of the bandwidth and there exists an optimal bandwidth to minimize the mean square error (MSE) locally. A data-driven variable bandwidth selection method, namely the intersection of confidence intervals (ICI), is adopted in LPR for adaptively determining the local optimal bandwidth that minimizes the MSE. Experimental results on simulated signals show that the LPR-ICI method can achieve robust and reliable performance in estimating time-varying covariance with different degrees of variations and under different noise scenarios, making it a powerful tool to study the dynamic relationship between non-stationary biomedical signals. Further, we apply the LPR-ICI method to estimate time-varying covariance of functional magnetic resonance imaging (fMRI) signals in a visual task for the inference of dynamic functional brain connectivity. The results show that the LPR-ICI method can effectively capture the transient connectivity patterns from fMRI.

An ICI Based Algorithm for Fast Denoising of Video Signals

In this paper, we have proposed a fast method for video denoising using the modified intersection of confidence intervals (ICI) rule, called fast ICI (FICI) method. The goal of the new FICI based video denoising method is to maintain an acceptable quality level of the denoised video estimate, and at the same time to significantly reduce denoising execution time when compared to the original ICI based method. The methods are tested on real-life video signals and their performances are analyzed and compared.It is shown that the FICI method outperforms the ICI method in terms of the execution time reduction by up to 96% (or up to 25 times). However, practical application demands dictate the choice of the video denoising method. If one wants fast denoising method with decent denoising results, the FICI based video denoising method is a better choice. The original ICI method, however, should be used in applications where significant noise suppression is an imperative regardless the computational complexity.