Stochastic resonance-based Raman spectroscopy denoising.

Rescaled three-mode principal component analysis: An approach to subspace recovery.

Ship acoustic signal classification is essential for vessel identification, underwater navigation, and maritime security. Traditional methods struggle with the non-stationary nature and noise of ship acoustic signals, reducing classification accuracy. To address these challenges, we propose an automated pipeline that integrates Empirical Mode Decomposition (EMD), adaptive wavelet filtering, feature selection, and a Bayesian-optimized Random Forest classifier. The framework begins with EMD-based decomposition, where the most informative Intrinsic Mode Functions (IMFs) are selected using Signal-to-Noise Ratio (SNR) analysis. Wavelet filtering is applied to reduce noise, with optimal wavelet parameters determined via SNR and Stein’s Unbiased Risk Estimate (SURE) criteria. Features extracted from statistical, frequency domain (FFT), and time–frequency (wavelet) metrics are ranked, and the top 11 most important features are selected for classification. A Bayesian-optimized Random Forest classifier is trained using the extracted features, ensuring optimal hyperparameter selection and reducing computational complexity. The classification results are further enhanced using a majority voting strategy, improving the accuracy of the final object identification. The proposed approach demonstrates high accuracy, improved noise suppression, and robust classification performance. The methodology is scalable, computationally efficient, and suitable for real-time maritime applications.

To examine the effect of incorporating self-supervised denoising as a pre-processing step for training deep learning (DL) based reconstruction methods on data corrupted by Gaussian noise. K-space data employed for training are typically multi-coil and inherently noisy. Although DL-based reconstruction methods trained on fully sampled data can enable high reconstruction quality, obtaining large, noise-free datasets is impractical. We leverage Generalized Stein's Unbiased Risk Estimate (GSURE) for denoising. We evaluate two DL-based reconstruction methods: Diffusion Probabilistic Models (DPMs) and Model-Based Deep Learning (MoDL). We evaluate the impact of denoising on the performance of these DL-based methods in solving accelerated multi-coil magnetic resonance imaging (MRI) reconstruction. The experiments were carried out on T2-weighted brain and fat-suppressed proton-density knee scans. We observed that self-supervised denoising enhances the quality and efficiency of MRI reconstructions across various scenarios. Specifically, employing denoised images rather than noisy counterparts when training DL networks results in lower normalized root mean squared error (NRMSE), higher structural similarity index measure (SSIM) and peak signal-to-noise ratio (PSNR) across different SNR levels, including 32, 22, and 12dB for T2-weighted brain data, and 24, 14, and 4dB for fat-suppressed knee data. We showed that denoising is an essential pre-processing technique capable of improving the efficacy of DL-based MRI reconstruction methods under diverse conditions. By refining the quality of input data, denoising enables training more effective DL networks, potentially bypassing the need for noise-free reference MRI scans.

Hyperspectral image (HSI) restoration is a challenging research area, covering a variety of inverse problems. Previous works have shown the great success of deep learning in HSI restoration. However, facing the problem of distribution gaps between training HSIs and target HSI, those data-driven methods falter in delivering satisfactory outcomes for the target HSIs. In addition, the degradation process of HSIs is usually disturbed by noise, which is not well taken into account in existing restoration methods. The existence of noise further exacerbates the dissimilarities within the data, rendering it challenging to attain desirable results without an appropriate learning approach. To track these issues, in this article, we propose a supervise-assisted self-supervised deep-learning method to restore noisy degraded HSIs. Initially, we facilitate the restoration network to acquire a generalized prior through supervised learning from extensive training datasets. Then, the self-supervised learning stage is employed and utilizes the specific prior of the target HSI. Particularly, to restore clean HSIs during the self-supervised learning stage from noisy degraded HSIs, we introduce a noise-adaptive loss function that leverages inner statistics of noisy degraded HSIs for restoration. The proposed noise-adaptive loss consists of Stein's unbiased risk estimator (SURE) and total variation (TV) regularizer and fine-tunes the network with the presence of noise. We demonstrate through experiments on different HSI tasks, including denoising, compressive sensing, super-resolution, and inpainting, that our method outperforms state-of-the-art methods on benchmarks under quantitative metrics and visual quality. The code is available at https://github.com/ying-fu/SSDL-HSI.

Large-Scale Graph Signal Denoising: A Heuristic Approach

Pc5 geomagnetic pulsations (PGPs) are ultra-low frequency (ULF) waves within the 1–7 mHz frequency band observed both in space and on the ground. PGPs offer versatile methods for studying the interaction between the magnetosphere and ionosphere in space. This study presents a comparative analysis of Pc5 pulsations observed in space and on the ground. The dataset used is the magnetic field-aligned readings obtained from the Geostationary Operational Environmental Satellite-10 (GOES-10) and ground-based magnetometer stations from the Svalbard network located in the auroral zone during solar cycle 23. Using the Empirical Mode Decomposition (EMD) method, we transformed the magnetic field time series from GOES-10 into the mean field-aligned coordinate system. PGPs were extracted from the toroidal component using a bandpass Butterworth filter. In addition, Pc5 waves were extracted from the Bx component of the ground magnetometer stations to enable effective comparison. Before conducting the comparative analysis, Pc5 events on the ground and in space were denoised using the heuristic Stein Unbiased Risk Estimate (SURE) approach with soft thresholding. Consequently, a good coherence between events from space and on the ground was observed, indicating the possibility of the same generation source. However, space-borne Pc5 events have a smaller average amplitude of 12 nT compared to Pc5 events observed on the ground, having an average amplitude of 139 nT. We attributed this difference in amplitude to the transformative mechanisms during the wave's propagation to the ground. The average percentage of occurrence of Pc5 geomagnetic pulsations observed in space was found to be 74%, and that on the ground was 92%. The percentage difference was found to be due to the spatial distribution of these waves. The integrity of the retrieved events was demonstrated by the strong correlation between the Kp index and events extracted from the ground magnetometer stations. Our results contribute significantly to the understanding of Pc5 geomagnetic pulsations within the space weather community. These findings will aid in developing forecasting and predictive models, enabling more effective studies of these waves and helping to mitigate their potential impacts on human activities and infrastructure.

Magnetic resonance imaging (MRI) can estimate tissue conductivity values using phase-based magnetic resonance electrical properties tomography (MR-EPT). However, this method is prone to noise amplification due to the Laplacian operator's sensitivity. To address this issue, we propose a novel unsupervised preprocessing denoiser for MRI transceive phase images. Our approach draws inspiration from the deep image prior (DIP) technique, utilizing the random initialization of a convolutional neural network (CNN) to enforce implicit regularization. Additionally, we incorporate Stein.s unbiased risk estimator (SURE) to optimize the network, which serves as an unbiased estimator of mean square error, thereby eliminating the need for labeled data. This modification mitigates the overfitting commonly associated with the DIP approach, enabling a fully unsupervised framework. Furthermore, we process real and imaginary images instead of phase images, aligning more closely with the theoretical basis of the risk estimator. Our generative model does not require pre-training or extensive training datasets, maintaining adaptability across different resolutions and signal-to-noise ratio levels. In our evaluations, the proposed method significantly reduced residual noise in phase maps, improving both quantitative and qualitative outcomes in phantom and simulated brain data. It also outperformed existing denoising techniques by reducing noise amplification and boundary errors. Applied to data from healthy volunteers and patients, our method yielded conductivity maps with reduced errors and values consistent with established literature. To our knowledge, this is the first blind, fully unsupervised approach capable of implementing a 2D phase-based MR-EPT reconstruction algorithm.

Diffusion-weighted imaging (DWI) is a magnetic resonance imaging (MRI) technique that provides information about the Brownian motion of water molecules within biological tissues. DWI plays a crucial role in stroke imaging and oncology, but its diagnostic value can be compromised by the inherently low signal-to-noise ratio (SNR). Conventional supervised deep learning-based denoising techniques encounter challenges in this domain as they necessitate noise-free target images for training. This work presents a novel approach for denoising and evaluating DWI scans in a self-supervised manner, eliminating the need for ground-truth data. By leveraging an adapted version of Stein’s unbiased risk estimator (SURE) and exploiting a phase-corrected combination of repeated acquisitions, we outperform both state-of-the-art self-supervised denoising methods and conventional non-learning-based approaches. Additionally, we demonstrate the applicability of our proposed approach in accelerating DWI scans by acquiring fewer image repetitions. To evaluate denoising performance, we introduce a self-supervised methodology that relies on analyzing the characteristics of the residual signal removed by the denoising approaches.

UIR-ES: An unsupervised underwater image restoration framework with equivariance and stein unbiased risk estimator

This paper addresses the problem of Bayesian wavelet estimating the mean vector of multivariate normal distribution under a multivariate normal prior distribution based on linear and nonlinear exponential balanced loss functions. The covariance matrix of multivariate normal distribution is considered known. Bayes estimators of mean vector parameter of multivariate normal distribution are achieved. Then two soft shrinkage wavelet threshold estimators based on Stein’s unbiased risk estimate (SURE) and Bayes estimators are provided. Finally, the performance of the soft shrinkage wavelet estimators was checked through simulation study and Electrical Grid Stability Simulated data set. Simulation and real data results showed the better performance of SURE thresholds based on linear and nonlinear exponential balanced loss functions compared to other classical wavelet methods. Also, they showed better performance for SURE threshold based on nonlinear exponential balanced loss function in multivariate normal distribution with small dimensions.

Truncated singular value decomposition (TSVD) is a popular recovery algorithm for multimode fiber single-pixel imaging (MMF-SPI), and it uses truncation thresholds to suppress noise influences. However, due to the sensitivity of MMF relative to stochastic disturbances, the threshold requires frequent re-determination as noise levels dynamically fluctuate. In response, we design an adaptive truncation threshold determination (ATTD) method for TSVD-based MMF-SPI in disturbed environments. Simulations and experiments reveal that ATTD approaches the performance of ideal clairvoyant benchmarks, and it corresponds to the best possible image recovery under certain noise levels and surpasses both traditional truncation threshold determination methods with less computation—fixed threshold and Stein’s unbiased risk estimator (SURE)—specifically under high noise levels. Moreover, target insensitivity is demonstrated via numerical simulations, and the robustness of the self-contained parameters is explored. Finally, we also compare and discuss the performance of TSVD-based MMF-SPI, which uses ATTD, and machine learning-based MMF-SPI, which uses diffusion models, to provide a comprehensive understanding of ATTD.

The matrix-variate normal distribution is a probability distribution that is a generalization of the multivariate normal distribution to matrix-valued random variables. In this paper, we introduce a wavelet shrinkage estimator based on Stein’s unbiased risk estimate (SURE) threshold for matrix-variate normal distribution. We find a new SURE threshold for soft thresholding wavelet shrinkage estimator under the reflected normal balanced loss function in low and high dimensional cases. Also, we obtain the restricted wavelet shrinkage estimator based on non-negative sub matrix of the mean matrix. Finally, we present a simulation study to test the validity of the wavelet shrinkage estimator and two real examples for low and high dimensional data sets.

Thermal noise caused by the imaged object is an intrinsic limitation in magnetic resonance imaging (MRI), resulting in an impaired clinical value of the acquisitions. Recently, deep learning (DL)-based denoising methods achieved promising results by extracting complex feature representations from large data sets. Most approaches are trained in a supervised manner by directly mapping noisy to noise-free ground-truth data and, therefore, require extensive paired data sets, which can be expensive or infeasible to obtain for medical imaging applications. In this work, a DL-based denoising approach is investigated which operates on complex-valued reconstructed magnetic resonance (MR) images without noise-free target data. An extension of Stein’s unbiased risk estimator (SURE) and spatially resolved noise maps quantifying the noise level with pixel accuracy were employed during the training process. Competitive denoising performance was achieved compared to supervised training with mean squared error (MSE) despite optimizing the model without noise-free target images. The proposed DL-based method can be applied for MR image enhancement without requiring noise-free target data for training. Integrating the noise maps as an additional input channel further enables the regulation of the desired level of denoising to adjust to the preference of the radiologist.

A machine learning approach combined with wavelet analysis for automatic detection of Pc5 geomagnetic pulsations observed at geostationary orbits

Abstract In multiple regression, when covariates are numerous, it is often reasonable to assume that only a small number of them has predictive information. In some medical applications for instance, it is believed that only a few genes out of thousands are responsible for cancer. In that case, the aim is not only to propose a good fit, but also to select the relevant covariates (genes). We propose to perform model selection with additive models in high dimensions (sample size and number of covariates). Our approach is computationally efficient thanks to fast wavelet transforms, it does not rely on cross validation, and it solves a convex optimization problem for a prescribed penalty parameter, called the quantile universal threshold. We also propose a second rule based on Stein unbiased risk estimation geared toward prediction. We use Monte Carlo simulations and real data to compare various methods based on false discovery rate (FDR), true positive rate (TPR) and mean squared error. Our approach is the only one to handle high dimensions, and has a good FDR–TPR trade‐off.

The estimation of mean vector parameters is very important in elliptical and spherically models. Among different methods, the Bayesian and shrinkage estimation are interesting. In this paper, the estimation of p-dimensional location parameter for p-variate elliptical and spherical distributions under an asymmetric loss function is investigated. We find generalized Bayes estimator of location parameters for elliptical and spherical distributions. Also we show the minimaxity and admissibility of generalized Bayes estimator in class of We introduce two new shrinkage soft-wavelet threshold estimators based on Huang shrinkage wavelet estimator (empirical) and Stein’s unbiased risk estimator (SURE) for elliptical and spherical distributions under non-linear exponential-balanced loss function. At the end, we present a simulation study to test the validity of the class of proposed estimators and physicochemical properties of the tertiary structure data set that is given to test the efficiency of this estimators in denoising.

Image reconstruction using deep learning algorithms offers improved reconstruction quality and lower reconstruction time than classical compressed sensing and model-based algorithms. Unfortunately, clean and fully sampled ground-truth data to train the deep networks is often unavailable in several applications, restricting the applicability of the above methods. We introduce a novel metric termed the ENsemble Stein's Unbiased Risk Estimate (ENSURE) framework, which can be used to train deep image reconstruction algorithms without fully sampled and noise-free images. The proposed framework is the generalization of the classical SURE and GSURE formulation to the setting where the images are sampled by different measurement operators, chosen randomly from a set. We evaluate the expectation of the GSURE loss functions over the sampling patterns to obtain the ENSURE loss function. We show that this loss is an unbiased estimate for the true mean-square error, which offers a better alternative to GSURE, which only offers an unbiased estimate for the projected error. Our experiments show that the networks trained with this loss function can offer reconstructions comparable to the supervised setting. While we demonstrate this framework in the context of MR image recovery, the ENSURE framework is generally applicable to arbitrary inverse problems.

Robust compressed sensing MRI based on combined nonconvex regularization

Deep external and internal learning for noisy compressive sensing