A Robust Noise Estimation Algorithm Based on Redundant Prediction and Local Statistics

Blind noise level estimation is a key issue in image processing applications that helps improve the visualization and perceptual quality of images. In this paper, we propose an improved block-based noise level estimation algorithm. The proposed algorithm first extracts homogenous patches from a single noisy image using local features, obtaining the covariance matrix eigenvalues of the patches, and constructs dynamic thresholds for outlier discrimination. By analyzing the correlations between scene complexity, noise strength, and other parameters, a nonlinear discriminant coefficient regression model is fitted to accurately predict the number of redundant dimensions and calculate the actual noise level according to the statistical properties of the elements in the redundancy dimension. The experimental results show that the accuracy and robustness of the proposed algorithm are better than those of the existing noise estimation algorithms in various scenes under different noise levels. It performs well overall in terms of performance and execution speed.

A robust t1 noise suppression method in NMR spectroscopy

Artefacts in high-resolution multidimensional nuclear magnetic resonance (NMR) spectra, known as t₁ noise, can significantly downgrade the spectral quality and remain a significant noise source, limiting the sensitivity of most two-dimensional NMR experiments. In addition to highly sensitive hardware and experimental designs, data post-processing is a relatively simple and cost-effective method for suppressing t₁ noise. In this study, histograms and quantiles were used to obtain a robust estimation of noise level. We constructed a weighted matrix to suppress the t₁ noise. The weighted matrix was calculated from the logistic functions, which were adaptively computed from the spectrum. The proposed method is robust and effective in both simulations and actual experiments. Further, it can maintain the quantitative relationship of the spectrogram, and is suitable for various complex peak types.

Sixty Years of Frequency-Domain Monaural Speech Enhancement: From Traditional to Deep Learning Methods

Frequency-domain monaural speech enhancement has been extensively studied for over 60 years, and a great number of methods have been proposed and applied to many devices. In the last decade, monaural speech enhancement has made tremendous progress with the advent and development of deep learning, and performance using such methods has been greatly improved relative to traditional methods. This survey paper first provides a comprehensive overview of traditional and deep-learning methods for monaural speech enhancement in the frequency domain. The fundamental assumptions of each approach are then summarized and analyzed to clarify their limitations and advantages. A comprehensive evaluation of some typical methods was conducted using the WSJ + Deep Noise Suppression (DNS) challenge and Voice Bank + DEMAND datasets to give an intuitive and unified comparison. The benefits of monaural speech enhancement methods using objective metrics relevant for normal-hearing and hearing-impaired listeners were evaluated. The objective test results showed that compression of the input features was important for simulated normal-hearing listeners but not for simulated hearing-impaired listeners. Potential future research and development topics in monaural speech enhancement are suggested.

[Low-dose helical CT projection data restoration using noise estimation]

OBJECTIVE

To build a helical CT projection data restoration model at random low-dose levels.

METHODS

We used a noise estimation module to achieve noise estimation and obtained a low-dose projection noise variance map, which was used to guide projection data recovery by the projection data restoration module. A filtering back-projection algorithm (FBP) was finally used to reconstruct the images. The 3D wavelet group residual dense network (3DWGRDN) was adopted to build the network architecture of the noise estimation and projection data restoration module using asymmetric loss and total variational regularization. For validation of the model, 1/10 and 1/15 of normal dose helical CT images were restored using the proposed model and 3 other restoration models (IRLNet, REDCNN and MWResNet), and the results were visually and quantitatively compared.

RESULTS

Quantitative comparisons of the restored images showed that the proposed helical CT projection data restoration model increased the structural similarity index by 5.79% to 17.46% compared with the other restoration algorithms (P < 0.05). The image quality scores of the proposed method rated by clinical radiologists ranged from 7.19% to 17.38%, significantly higher than the other restoration algorithms (P < 0.05).

CONCLUSION

The proposed method can effectively suppress noises and reduce artifacts in the projection data at different low-dose levels while preserving the integrity of the edges and fine details of the reconstructed CT images.

Low Complexity Robust Data Demodulation for GNSS

In this article, we provide closed-form approximations of log-likelihood ratio (LLR) values for direct sequence spread spectrum (DS-SS) systems over three particular scenarios, which are commonly found in the Global Navigation Satellite System (GNSS) environment. Those scenarios are the open sky with smooth variation of the signal-to-noise ratio (SNR), the additive Gaussian interference, and pulsed jamming. In most of the current communications systems, block-wise estimators are considered. However, for some applications such as GNSSs, symbol-wise estimators are available due to the low data rate. Usually, the noise variance is considered either perfectly known or available through symbol-wise estimators, leading to possible mismatched demodulation, which could induce errors in the decoding process. In this contribution, we first derive two closed-form expressions for LLRs in additive white Gaussian and Laplacian noise channels, under noise uncertainty, based on conjugate priors. Then, assuming those cases where the statistical knowledge about the estimation error is characterized by a noise variance following an inverse log-normal distribution, we derive the corresponding closed-form LLR approximations. The relevance of the proposed expressions is investigated in the context of the GPS L1C signal where the clock and ephemeris data (CED) are encoded with low-density parity-check (LDPC) codes. Then, the CED is iteratively decoded based on the belief propagation (BP) algorithm. Simulation results show significant frame error rate (FER) improvement compared to classical approaches not accounting for such uncertainty.

A Robust INS/SRS/CNS Integrated Navigation System with the Chi-Square Test-Based Robust Kalman Filter

In order to achieve a highly autonomous and reliable navigation system for aerial vehicles that involves the spectral redshift navigation system (SRS), the inertial navigation (INS)/spectral redshift navigation (SRS)/celestial navigation (CNS) integrated system is designed and the spectral-redshift-based velocity measurement equation in the INS/SRS/CNS system is derived. Furthermore, a new chi-square test-based robust Kalman filter (CSTRKF) is also proposed in order to improve the robustness of the INS/SRS/CNS navigation system. In the CSTRKF, the chi-square test (CST) not only detects measurements with outliers and in non-Gaussian distributions, but also estimates the statistical characteristics of measurement noise. Finally, the results of our simulations indicate that the INS/SRS/CNS integrated navigation system with the CSTRKF possesses strong robustness and high reliability.

Rough or Noisy? Metrics for Noise Estimation in SfM Reconstructions

Structure from Motion (SfM) can produce highly detailed 3D reconstructions, but distinguishing real surface roughness from reconstruction noise and geometric inaccuracies has always been a difficult problem to solve. Existing SfM commercial solutions achieve noise removal by a combination of aggressive global smoothing and the reconstructed texture for smaller details, which is a subpar solution when the results are used for surface inspection. Other noise estimation and removal algorithms do not take advantage of all the additional data connected with SfM. We propose a number of geometrical and statistical metrics for noise assessment, based on both the reconstructed object and the capturing camera setup. We test the correlation of each of the metrics to the presence of noise on reconstructed surfaces and demonstrate that classical supervised learning methods, trained with these metrics can be used to distinguish between noise and roughness with an accuracy above 85%, with an additional 5-6% performance coming from the capturing setup metrics. Our proposed solution can easily be integrated into existing SfM workflows as it does not require more image data or additional sensors. Finally, as part of the testing we create an image dataset for SfM from a number of objects with varying shapes and sizes, which are available online together with ground truth annotations.

Processing APT Spectral Backgrounds for Improved Quantification

We describe a method to estimate background noise in atom probe tomography (APT) mass spectra and to use this information to enhance both background correction and quantification. Our approach is mathematically general in form for any detector exhibiting Poisson noise with a fixed data acquisition time window, at voltages varying through the experiment. We show that this accurately estimates the background observed in real experiments. The method requires, as a minimum, the z-coordinate and mass-to-charge-state data as input and can be applied retrospectively. Further improvements are obtained with additional information such as acquisition voltage. Using this method allows for improved estimation of variance in the background, and more robust quantification, with quantified count limits at parts-per-million concentrations. To demonstrate applications, we show a simple peak detection implementation, which quantitatively suppresses false positives arising from random noise sources. We additionally quantify the detectability of 121-Sb in a standardized-doped Si microtip as (1.5 × 10−5, 3.8 × 10−5) atomic fraction, α = 0.95. This technique is applicable to all modes of APT data acquisition and is highly general in nature, ultimately allowing for improvements in analyzing low ionic count species in datasets.

Acoustic Impulsive Noise Based on Non-Gaussian Models: An Experimental Evaluation

In general, acoustic channels are not Gaussian distributed neither are second-order stationary. Considering them for signal processing methods designed for Gaussian assumptions is inadequate, consequently yielding in poor performance of such methods. This paper presents an analysis for audio signal corrupted by impulsive noise using non-Gaussian models. Audio samples are compared to the Gaussian, α-stable and Gaussian mixture models, evaluating the fitting by graphical and numerical methods. We discuss fitting properties as the window length and the overlap, finally concluding that the α-stable model has the best fit for all tested scenarios.

Noise Estimation for Image Sensor Based on Local Entropy and Median Absolute Deviation

Noise estimation for image sensor is a key technique in many image pre-processing applications such as blind de-noising. The existing noise estimation methods for additive white Gaussian noise (AWGN) and Poisson-Gaussian noise (PGN) may underestimate or overestimate the noise level in the situation of a heavy textured scene image. To cope with this problem, a novel homogenous block-based noise estimation method is proposed to calculate these noises in this paper. Initially, the noisy image is transformed into the map of local gray statistic entropy (LGSE), and the weakly textured image blocks can be selected with several biggest LGSE values in a descending order. Then, the Haar wavelet-based local median absolute deviation (HLMAD) is presented to compute the local variance of these selected homogenous blocks. After that, the noise parameters can be estimated accurately by applying the maximum likelihood estimation (MLE) to analyze the local mean and variance of selected blocks. Extensive experiments on synthesized noised images are induced and the experimental results show that the proposed method could not only more accurately estimate the noise of various scene images with different noise levels than the compared state-of-the-art methods, but also promote the performance of the blind de-noising algorithm.

Tensor decomposition and non-local means based spectral CT image denoising

BACKGROUNDAs one type of the state-of-the-art detectors, photon counting detectors are used in spectral computed tomography (CT) to classify the received photons into several energy channels and generate multichannel projections simultaneously. However, FBP reconstructed images contain severe noise due to the low photon counts in each energy channel.OBJECTIVEA spectral CT image denoising method based on tensor-decomposition and non-local means (TDNLM) is proposed.METHODSIn a CT image, it is widely accepted that there exists self-similarity over the spatial domain. In addition, because a multichannel CT image is obtained from the same object at different energies, images among different channels are highly correlated. Motivated by these two characteristics of the spectral CT images, tensor decomposition and non-local means are employed to recover fine structures in spectral CT images. Moreover, images in all energy channels are added together to form a high signal-to-noise ratio image, which is applied to encourage the signal preservation of the TDNLM. The combination of TD, NLM and the guidance of a high-quality image enhances the low-dose spectral CT, and a parameter selection strategy is designed to achieve the optimal image quality.RESULTSThe effectiveness of the developed algorithm is validated on both numerical simulations and realistic preclinical applications. The root mean square error (RMSE) and the structural similarity (SSIM) are used to quantitatively assess the image quality. The proposed method successfully restored high-quality images (average RMSE=0.0217 cm-1 and SSIM=0.987) from noisy spectral CT images (average RMSE=0.225 cm-1 and SSIM=0.633). In addition, RMSE of each decomposed material component is also remarkably reduced. Compared to the state-of-the-art iterative spectral CT reconstruction algorithms, the proposed method achieves comparable performance with dramatically reduced computational cost, resulting in a speedup of >50.CONCLUSIONSThe outstanding denoising performance, the high computational efficiency and the adaptive parameter selection strategy make the proposed method practical for spectral CT applications.

Adaptive tuning piecewise cubic Hermite interpolation with Wiener filter in wavelet domain for scanning electron microscope images

Image processing is introduced to remove or reduce the noise and unwanted signal that deteriorate the quality of an image. Here, a single level two-dimensional wavelet transform is applied to the image in order to obtain the wavelet transform sub-band signal of an image. An estimation technique to predict the noise variance in an image is proposed, which is then fed into a Wiener filter to filter away the noise from the sub-band of the image. The proposed filter is called adaptive tuning piecewise cubic Hermite interpolation with Wiener filter in the wavelet domain. The performance of this filter is compared with four existing filters: median filter, Gaussian smoothing filter, two level wavelet transform with Wiener filter and adaptive noise Wiener filter. Based on the results, the adaptive tuning piecewise cubic Hermite interpolation with Wiener filter in wavelet domain has better performance than the other four methods.

Computation of exact g-factor maps in 3D GRAPPA reconstructions

PURPOSE

To characterize the noise distributions in 3D-MRI accelerated acquisitions reconstructed with GRAPPA using an exact noise propagation analysis that operates directly in k-space.

THEORY AND METHODS

We exploit the extensive symmetries and separability in the reconstruction steps to account for the correlation between all the acquired k-space samples. Monte Carlo simulations and multi-repetition phantom experiments were conducted to test both the accuracy and feasibility of the proposed method; a high-resolution in-vivo experiment was performed to assess the applicability of our method to clinical scenarios.

RESULTS

Our theoretical derivation shows that the direct k-space analysis renders an exact noise characterization under the assumptions of stationarity and uncorrelation in the original k-space. Simulations and phantom experiments provide empirical support to the theoretical proof. Finally, the high-resolution in-vivo experiment demonstrates the ability of the proposed method to assess the impact of the sub-sampling pattern on the overall noise behavior.

CONCLUSIONS

By operating directly in the k-space, the proposed method is able to provide an exact characterization of noise for any Cartesian pattern sub-sampled along the two phase-encoding directions. Exploitation of the symmetries and separability into independent blocks through the image reconstruction procedure allows us to overcome the computational challenges related to the very large size of the covariance matrices involved.

Poisson-Gaussian Noise Analysis and Estimation for Low-Dose X-ray Images in the NSCT Domain

The noise distribution of images obtained by X-ray sensors in low-dosage situations can be analyzed using the Poisson and Gaussian mixture model. Multiscale conversion is one of the most popular noise reduction methods used in recent years. Estimation of the noise distribution of each subband in the multiscale domain is the most important factor in performing noise reduction, with non-subsampled contourlet transform (NSCT) representing an effective method for scale and direction decomposition. In this study, we use artificially generated noise to analyze and estimate the Poisson–Gaussian noise of low-dose X-ray images in the NSCT domain. The noise distribution of the subband coefficients is analyzed using the noiseless low-band coefficients and the variance of the noisy subband coefficients. The noise-after-transform also follows a Poisson–Gaussian distribution, and the relationship between the noise parameters of the subband and the full-band image is identified. We then analyze noise of actual images to validate the theoretical analysis. Comparison of the proposed noise estimation method with an existing noise reduction method confirms that the proposed method outperforms traditional methods.

An Adaptive Deghosting Method in Neural Network-Based Infrared Detectors Nonuniformity Correction

The problems of the neural network-based nonuniformity correction algorithm for infrared focal plane arrays mainly concern slow convergence speed and ghosting artifacts. In general, the more stringent the inhibition of ghosting, the slower the convergence speed. The factors that affect these two problems are the estimated desired image and the learning rate. In this paper, we propose a learning rate rule that combines adaptive threshold edge detection and a temporal gate. Through the noise estimation algorithm, the adaptive spatial threshold is related to the residual nonuniformity noise in the corrected image. The proposed learning rate is used to effectively and stably suppress ghosting artifacts without slowing down the convergence speed. The performance of the proposed technique was thoroughly studied with infrared image sequences with both simulated nonuniformity and real nonuniformity. The results show that the deghosting performance of the proposed method is superior to that of other neural network-based nonuniformity correction algorithms and that the convergence speed is equivalent to the tested deghosting methods.

Feasibility of reduced-dose three-dimensional/four-dimensional-digital subtraction angiogram using a weighted edge preserving filter

A conventional three-dimensional/four-dimensional (3D/4D) digital subtraction angiogram (DSA) requires two rotational acquisitions (mask and fill) to compute the log-subtracted projections that are used to reconstruct a 3D/4D volume. Since all of the vascular information is contained in the fill acquisition, it is hypothesized that it is possible to reduce the x-ray dose of the mask acquisition substantially and still obtain subtracted projections adequate to reconstruct a 3D/4D volume with noise level comparable to a full-dose acquisition. A full-dose mask and fill acquisition were acquired from a clinical study to provide a known full-dose reference reconstruction. Gaussian noise was added to the mask acquisition to simulate a mask acquisition acquired at 10% relative dose. Noise in the low-dose mask projections was reduced with a weighted edge preserving filter designed to preserve bony edges while suppressing noise. Two-dimensional (2D) log-subtracted projections were computed from the filtered low-dose mask and full-dose fill projections, and then 3D/4D-DSA reconstruction algorithms were applied. Additional bilateral filtering was applied to the 3D volumes. The signal-to-noise ratio measured in the filtered 3D/4D-DSA volumes was compared to the full-dose case. The average ratio of filtered low-dose SNR to full-dose SNR was 0.856 for the 3D-DSA and 0.849 for the 4D-DSA, indicating that the method is a feasible approach to restoring SNR in DSA scans acquired with a low-dose mask. The method was also tested in a phantom study with full-dose fill and 22%-dose mask.

Noise Estimation in Electroencephalogram Signal by Using Volterra Series Coefficients

The Volterra model is widely used for nonlinearity identification in practical applications. In this paper, we employed Volterra model to find the nonlinearity relation between electroencephalogram (EEG) signal and the noise that is a novel approach to estimate noise in EEG signal. We show that by employing this method. We can considerably improve the signal to noise ratio by the ratio of at least 1.54. An important issue in implementing Volterra model is its computation complexity, especially when the degree of nonlinearity is increased. Hence, in many applications it is urgent to reduce the complexity of computation. In this paper, we use the property of EEG signal and propose a new and good approximation of delayed input signal to its adjacent samples in order to reduce the computation of finding Volterra series coefficients. The computation complexity is reduced by the ratio of at least 1/3 when the filter memory is 3.

A g-factor metric for k-t SENSE and k-t PCA based parallel imaging

PURPOSE

To propose and validate a g-factor formalism for k-t SENSE, k-t PCA and related k-t methods for assessing SNR and temporal fidelity.

METHODS

An analytical gxf -factor formulation in the spatiotemporal frequency domain is derived, enabling assessment of noise and depiction fidelity in both the spatial and frequency domain. Using pseudoreplica analysis of cardiac cine data the gxf -factor description is validated and example data are used to analyze the performance of k-t methods for various parameter settings.

RESULTS

Analytical gxf -factor maps were found to agree well with pseudoreplica analysis for 3x, 5x, and 7x k-t SENSE and k-t PCA. While k-t SENSE resulted in lower average gxf values (gx (avg) ) in static regions when compared with k-t PCA, k-t PCA yielded lower gx (avg) values in dynamic regions. Temporal transfer was better preserved with k-t PCA for increasing undersampling factors.

CONCLUSION

The proposed gxf -factor and temporal transfer formalism allows assessing noise performance and temporal depiction fidelity of k-t methods including k-t SENSE and k-t PCA. The framework enables quantitative comparison of different k-t methods relative to frame-by-frame parallel imaging reconstruction.

Noise estimation from averaged diffusion weighted images: Can unbiased quantitative decay parameters assist cancer evaluation?

PURPOSE

Multiexponential decay parameters are estimated from diffusion-weighted-imaging that generally have inherently low signal-to-noise ratio and non-normal noise distributions, especially at high b-values. Conventional nonlinear regression algorithms assume normally distributed noise, introducing bias into the calculated decay parameters and potentially affecting their ability to classify tumors. This study aims to accurately estimate noise of averaged diffusion-weighted-imaging, to correct the noise induced bias, and to assess the effect upon cancer classification.

METHODS

A new adaptation of the median-absolute-deviation technique in the wavelet-domain, using a closed form approximation of convolved probability-distribution-functions, is proposed to estimate noise. Nonlinear regression algorithms that account for the underlying noise (maximum probability) fit the biexponential/stretched exponential decay models to the diffusion-weighted signal. A logistic-regression model was built from the decay parameters to discriminate benign from metastatic neck lymph nodes in 40 patients.

RESULTS

The adapted median-absolute-deviation method accurately predicted the noise of simulated (R(2)  = 0.96) and neck diffusion-weighted-imaging (averaged once or four times). Maximum probability recovers the true apparent-diffusion-coefficient of the simulated data better than nonlinear regression (up to 40%), whereas no apparent differences were found for the other decay parameters.

CONCLUSIONS

Perfusion-related parameters were best at cancer classification. Noise-corrected decay parameters did not significantly improve classification for the clinical data set though simulations show benefit for lower signal-to-noise ratio acquisitions.

Comprehensive framework for accurate diffusion MRI parameter estimation

During the last decade, many approaches have been proposed for improving the estimation of diffusion measures. These techniques have already shown an increase in accuracy based on theoretical considerations, such as incorporating prior knowledge of the data distribution. The increased accuracy of diffusion metric estimators is typically observed in well-defined simulations, where the assumptions regarding properties of the data distribution are known to be valid. In practice, however, correcting for subject motion and geometric eddy current deformations alters the data distribution tremendously such that it can no longer be expressed in a closed form. The image processing steps that precede the model fitting will render several assumptions on the data distribution invalid, potentially nullifying the benefit of applying more advanced diffusion estimators. In this work, we present a generic diffusion model fitting framework that considers some statistics of diffusion MRI data. A central role in the framework is played by the conditional least squares estimator. We demonstrate that the accuracy of that particular estimator can generally be preserved, regardless the applied preprocessing steps, if the noise parameter is known a priori. To fulfill that condition, we also propose an approach for the estimation of spatially varying noise levels.

Implementation of the Rauch-Tung-Striebel smoother for sensor compatibility correction of a fixed-wing unmanned air vehicle

This paper presents a complete procedure for sensor compatibility correction of a fixed-wing Unmanned Air Vehicle (UAV). The sensors consist of a differential air pressure transducer for airspeed measurement, two airdata vanes installed on an airdata probe for angle of attack (AoA) and angle of sideslip (AoS) measurement, and an Attitude and Heading Reference System (AHRS) that provides attitude angles, angular rates, and acceleration. The procedure is mainly based on a two pass algorithm called the Rauch-Tung-Striebel (RTS) smoother, which consists of a forward pass Extended Kalman Filter (EKF) and a backward recursion smoother. On top of that, this paper proposes the implementation of the Wiener Type Filter prior to the RTS in order to avoid the complicated process noise covariance matrix estimation. Furthermore, an easy to implement airdata measurement noise variance estimation method is introduced. The method estimates the airdata and subsequently the noise variances using the ground speed and ascent rate provided by the Global Positioning System (GPS). It incorporates the idea of data regionality by assuming that some sort of statistical relation exists between nearby data points. Root mean square deviation (RMSD) is being employed to justify the sensor compatibility. The result shows that the presented procedure is easy to implement and it improves the UAV sensor data compatibility significantly.