Noise Level Estimation Research Articles

Asymmetric learning based deep denoiser for nonstationary desert seismic noise suppression

Random noise in desert seismic data has the weak similarity to the effective signals and spatiotemporally variable noise intensity. Mismatch noise intensity degrades the denoising performance of the convolutional neural network in incomplete noise suppression and damaged seismic signals. We propose an asymmetric learning-based nonstationary convolutional denoising neural network (AL-NCDNet) by introducing an asymmetric loss function and the noise level (NL) estimation block. Since the denoised result is robust to the overestimated NL and more sensitive to the underestimated NL, an asymmetric learning framework is adopted by leveraging a weighted loss function for constraining the noise level estimation block. Under the asymmetric learning framework, more penalties are imposed on the underestimated NL than the overestimated ones, alleviating the problem of noise residue caused by underestimated NL. Moreover, the estimated NL is taken as the weight between noise suppression and signal fidelity to guide the main denoising block adaptively suppressing nonstationary noise. The AL-NCDNet is tested on the synthetic, public and field seismic data. The denoised results verify that asymmetric learning is able to improve the accuracy of the estimated NL and the efficiency of the denoising model, thereby allows AL-NCDNet to effectively suppress spatiotemporally variable noise while preserving seismic events.

Noise Estimation and Type Identification in Natural Scene and Medical Images using Deep Learning Approaches

The image enhancement for the natural images is the vast field where the quality of the images degrades based on the capturing and processing methods employed by the capturing devices. Based on noise type and estimation of noise, filter need to be adopted for enhancing the quality of the image. In the same manner, the medical field also needs some filtering mechanism to reduce the noise and detection of the disease based on the clarity of the image captured; in accordance with it, the preprocessing steps play a vital role to reduce the burden on the radiologist to make the decision on presence of disease. Based on the estimated noise and its type, the filters are selected to delete the unwanted signals from the image. Hence, identifying noise types and denoising play an important role in image analysis. The proposed framework addresses the noise estimation and filtering process to obtain the enhanced images. This paper estimates and detects the noise types, namely Gaussian, motion artifacts, Poisson, salt-andpepper, and speckle noises. Noise is estimated by using discrete wavelet transformation (DWT). This separates the image into quadruple sub-bands. Noise and HH sub-band are high-frequency components. HH sub-band also has vertical edges. These vertical edges are removed by performing Hadamard operation on downsampled Sobel edge-detected image and HH sub-band. Using HH sub-band after removing vertical edges is considered for estimating the noise. The Rician energy equation is used to estimate the noise. This is given as input for Artificial Neural Network to improve the estimated noise level. For identifying noise type, CNN is used. After removing vertical edges, the HH sub-band is given to the CNN model for classification. The classification accuracy results of identifying noise type are 100% on natural images and 96.3% on medical images.

Smart mobility procedure for road traffic noise dynamic estimation by video analysis

Road Traffic Noise is a major concern in Europe, with more than 20% of people exposed to harmful noise levels. Efficient monitoring and assessment of the sound levels in critical areas are crucial to support decision strategies to control/reduce noise exposure. However, continuous and long-time ranged spatio-temporal measurements require high-cost equipment and maintenance duties. Therefore, this paper aims to develop a cost-efficient smart mobility procedure for the estimation of traffic noise levels based on roadside video images. The developed procedure involves an algorithm that extracts traffic volumes, identifies vehicle classes, estimates each vehicle’s speed from video recordings, and a noise assessment component using dynamic microscopic models. These latter are based on existing Noise Emission Models – NEMs, for the assessment of the source sound power levels, coupled with a sound propagation model able to consider each on-road vehicle speed as input and evaluate the equivalent continuous A-weighted sound pressure levels. The developed approach is characterized by a modular structure that easily allows to replace NEMs and/or incorporate extra variables in the sound propagation model. The procedure is tested on a rural road of a medium-sized city, under different levels of service, and results show that the errors concerning the noise estimations are below 1 dBA, revealing high accuracy.

Denoising Generalization Performance of Channel Estimation in Multipath Time-Varying OFDM Systems

Although Orthogonal Frequency Division Multiplexing (OFDM) technology is still the key transmission waveform technology in 5G, traditional channel estimation algorithms are no longer sufficient for the high-speed multipath time-varying channels faced by both existing 5G and future 6G. In addition, the existing Deep Learning (DL) based OFDM channel estimators are only applicable to Signal-to-Noise Ratios (SNRs) in a small range, and the estimation performance of the existing algorithms is greatly limited when the channel model or the mobile speed at the receiver does not match. To solve this problem, this paper proposes a novel network model NDR-Net that can be used for channel estimation under unknown noise levels. NDR-Net consists of a Noise Level Estimate subnet (NLE), a Denoising Convolutional Neural Network subnet (DnCNN), and a Residual Learning cascade. Firstly, a rough channel estimation matrix value is obtained using the conventional channel estimation algorithm. Then it is modeled as an image and input to the NLE subnet for noise level estimation to obtain the noise interval. Then it is input to the DnCNN subnet together with the initial noisy channel image for noise reduction to obtain the pure noisy image. Finally, the residual learning is added to obtain the noiseless channel image. The simulation results show that NDR-Net can obtain better estimation results than traditional channel estimation, and it can be well adapted when the SNR, channel model, and movement speed do not match, which indicates its superior engineering practicability.

Monitoring of traffic noise pollution in urban Patna, Bihar, India

Road traffic noise is a major environmental issue that has been faced by many people around the world, including in Patna city. There is a need to investigate noise regularly because of the rapidly increasing traffic volume. This study focuses on the estimation of the urban traffic noise level in Patna, Bihar, India. Based on a preliminary survey of traffic volume, 12 stations were selected. A sound meter was used to measure the “A”-weighted noise level. Noise parameters like L10, L50, and L90 were evaluated from the collected noise data. And these noise parameters were used for the calculation of noise pollution indices like Noise Climate (NC), Equivalent Continuous Noise Level (Leq), Noise Pollution Level (NPL), and Traffic Noise Index (TNI). These noise indices compare with the standard limit of the Central Pollution Control Board (CPCB). The equivalent continuous noise level (Leq) measured at different locations in the commercial cum residential zones varies from 77.7 dBA to 92.5 dBA, which is higher than the prescribed noise level limit of the CPCB. Other noise indices, such as the NPL and TNI, are found to range from 88.2 dBA to 111.5 dBA and 77.9 dBA to 125.9 dBA, respectively, at various sampling locations and are also higher than the prescribed limit of the CPCB. The noise level of all stations was found to exceed the prescribed limit of the CPCB. There is a strong correlation exists between NPL with TNI and NC (r > 0.5). Also, there is a strong correlation exists between Leq with NPL (r > 0.5). Using NPL as a dependent variable and TNI, NC, and Leq as independent variables, the regression model was completely validated.

PILN: A posterior information learning network for blind reconstruction of lung CT images

Background and objective:Computer tomography (CT) imaging technology has played significant roles in the diagnosis and treatment of various lung diseases, but the degradations in CT images usually cause the loss of detailed structural information and interrupt the judgement from clinicians. Therefore, reconstructing noise-free, high-resolution CT images with sharp details from degraded ones is of great importance for the computer-assisted diagnosis (CAD) system. However, current image reconstruction methods suffer from unknown parameters of multiple degradations in actual clinical images.Methods:To solve these problems, we propose a unified framework, so called Posterior Information Learning Network (PILN), for blind reconstruction of lung CT images. The framework consists of two stages: Firstly, a noise level learning (NLL) network is proposed to quantify the Gaussian and artifact noise degradations into different levels. Inception-residual modules are designed to extract multi-scale deep features from the noisy image, and residual self-attention structures are proposed to refine deep features to essential representations of noise. Secondly, by taking the estimated noise levels as prior information, a cyclic collaborative super-resolution (CyCoSR) network is proposed to iteratively reconstruct the high-resolution CT image and estimate the blur kernel. Two convolutional modules are designed based on cross-attention transformer structure, named as Reconstructor and Parser. The high-resolution image is restored from the degraded image by the Reconstructor under the guidance of the predicted blur kernel, while the blur kernel is estimated by the Parser according to the reconstructed image and the degraded one. The NLL and CyCoSR networks are formulated as an end-to-end framework to handle multiple degradations simultaneously.Results:The proposed PILN is applied to the Cancer Imaging Archive (TCIA) dataset and the Lung Nodule Analysis 2016 Challenge (LUNA16) dataset to evaluate its ability in reconstructing lung CT images. Compared with the state-of-the-art image reconstruction algorithms, it can provide high-resolution images with less noise and sharper details with respect to quantitative benchmarks.Conclusions:Extensive experimental results demonstrate that our proposed PILN can achieve better performance on blind reconstruction of lung CT images, providing noise-free, detail-sharp and high-resolution images without knowing the parameters of multiple degradation sources.

A machine learning- and compressed sensing-based approach for surrogate modelling in environmental acoustics: towards fast evaluation of building façade road traffic noise levels

State-of-the-art urban road traffic noise propagation simulation methods such as the CNOSSOS-EU framework rely on ray tracing to estimate noise levels at specific locations on façades, so-called receiver points; this method is computationally expensive and its cost increases with the number of receiver points, which limits the spatial accuracy of such simulations in the context of real-time or near-real-time urban noise simulation applications. This contribution aims to investigate the applicability of multiple data-driven methods to the surrogate modelling of traffic noise propagation for fast façade noise calculation as an alternative to these traditional, ray-tracing-based methods. The proposed approach uses compressed sensing to select a small subset of receiver points from which the data set of the entire façade may be reconstructed, associated with a Kriging model and neural networks, used to predict noise levels for these sensors. The prediction performance of each of these steps is evaluated on an academic test case, with two levels of complexity based on the dimensionality of the problem.

Block Chain Based Underwater Communication Using Li-Fi and Eliminating Noise Using Machine Learning

Underwater medium is the most difficult medium for data communication while Electromagnetic waves, acoustic waves, and optical signals are some of the present modes of communication in water. Electromagnetic waves would suffer a significant loss, limiting them to short-range communication; optical waves on the other hand, have line-of-sight concerns. The proposed work employs a Light Fidelity (Li-Fi) data transmission technology in a water medium to address these issues. Visible light communication allows to use a wide range of frequencies to send messages, when compared to other transmission technologies, the data transfer rate is likewise relatively high. Electronic components and level converters are utilized to regulate flickering and communicate data on both the transmitter and receiver sides, when exposed to the outer environment, it will lose the signal due to noise. To help with noise level estimate and signal reconstruction, the proposed work employs a machine learning technique that uses an encrypted block chain approach to check for data loss and a weighted Long Short-Term Memory (LSTM) algorithm to predict data from a Neural Network. The proposed work concludes that block chain can be the best way for data transfer in terms of minimizing errors while maintaining high accuracy.

A Self-Supervised Denoising Method Based on Deep Noise Estimation

Seismic random noise attenuation is an essential procedure when processing seismic data. Due to various acquisition environments and complex geological conditions, random noise in seismic field data exhibits spatiotemporal levels, significantly increasing the difficulty of extracting seismic signals. The deep learning (DL) methods have shown excellent performances for seismic denoising. However, most existing discriminative DL methods cannot fit field data with noise levels and signal structures that differ from the training set. To tackle the unmatching challenge, we propose a self-supervised deep denoising model named noise estimation-based convolution neural network (NE-CNN), which contains a multiscale denoising module as a pretrained model and a dual-path noise estimation module that estimates the noise level of each data patch with a generalized Gaussian distribution and gray-level co-occurrence matrix (GLCM). With Stein’s unbiased risk estimate (SURE), we can fine-tune the pretrained denoising module according to the estimated noise levels in a self-supervised style solely on data to be processed, leading to a boost of robustness to nonstationary seismic noise. In synthetic and field data tests, NE-CNN performed satisfactorily compared with discriminative DL methods in denoising effects on seismic data with nonstationary noise.

Remote Sensing Image Recovery and Enhancement by Joint Blind Denoising and Dehazing

Due to the hazy weather and the long-distance imaging path, the captured remote sensing image (RSI) may suffer from detail loss and noise pollution. However, simply applying dehazing operation on a noisy hazy image may result in noise amplification. Therefore, in this paper, we propose joint blind denoising and dehazing for RSI recovery and enhancement to address this problem. Firstly, we propose an efficient and effective noise level estimation method based on quad-tree subdivision and integrate it into FFDNet for blind denoising. Secondly, a multi-scale guided filter decomposes the denoised hazy image into base and detailed layers, separating the initial details. Then, the dehazing procedure using the corrected boundary constraint is implemented in the base layer, while a nonlinear sigmoid mapping function enhances the detailed layers. The last step is to fuse the enhanced detailed layers and the dehazed base layer to get the final result. Using both synthetic remote sensing hazy image (RSHI) datasets and real-world RSHI, we perform comprehensive experiments to evaluate the proposed method. Results show that our method is superior to well-known methods in both dehazing and joint denoising and dehazing tasks.

Residual in Residual Scaling Networks for Polarimetric SAR Image Despeckling

Speckle reduction is a longstanding topic for polarimetric synthetic aperture radar (PolSAR) images. In this paper, we propose a novel end-to-end PolSAR image despeckling framework for the first time, which predicts the weight matrices of neighboring pixels instead of the target pixel itself nor the nor the noise, to achieve image despeckling. It hardly relies on any assumptions on the speckle noise distribution. Within this framework, residual in residual scaling network (RIRSN) is developed by combining the advantages of residual connections and residual scaling. To reduce network redundancy further, a dynamic version of RIRSN (DRIRSN) is also proposed by adjusting the network structure dynamically based on noise level and image content. Specifically, in DRIRSN, we introduce a lightweight network called picture2vector to estimate noise level, and a well-designed loss function to estimate image information level and measure image denoising quality simultaneously. The proposed picture2vector and loss function guide DRIRSN to focus on image areas with rich content and information, enhancing the adaptability of the network. DRIRSN inherits the properties of RIRSN for adaptively selecting and weighting the pixels of the neighborhood, and dynamically adjusts the network structure according to the estimated noise level and image content. We compare the proposed networks with reference methods on both simulated images and real images. Experimental results demonstrate that the proposed networks can effectively reduce speckle noise with low time consumption and, meanwhile, better preserve the details and the repetitive structures such as textures and edges, and the polarimetric scattering characteristics, compared with the other methods.

Maximum Likelihood Estimation in Data-Driven Modeling and Control

Recently, various algorithms for data-driven simulation and control have been proposed based on the Willems’ fundamental lemma. However, when collected data are noisy, these methods lead to ill-conditioned data-driven model structures. In this article, we present a maximum likelihood framework to obtain an optimal data-driven model, the signal matrix model, in the presence of output noise. Data compression and noise-level estimation schemes are also proposed to apply the algorithm efficiently to large datasets and unknown noise-level scenarios. Two approaches in system identification and receding horizon control are developed based on the derived optimal estimator. The first one identifies a finite impulse response model. This approach improves the least-squares estimator with less restrictive assumptions. The second one applies the signal matrix model as the predictor in predictive control. The control performance is shown to be better than existing data-driven predictive control algorithms, especially under high noise levels. Both approaches demonstrate that the derived estimator provides a promising framework to apply data-driven algorithms to noisy data.

Bayesian Linear Seismic Inversion Integrating Uncertainty of Noise Level Estimation and Wavelet Extraction

Seismic impedance inversion is an important method to identify the spatial characteristics of underground rock physical properties. Seismic inversion results and uncertainty evaluation are the important scientific basis for risk decision-making in oil and gas development. Under the assumption that the impedance and the error of the observed seismic data meet the Gaussian distribution or log–Gaussian distribution, the Bayesian linear seismic inversion can analytically obtain the posterior probability distribution of impedance. However, errors from observation, calculation, model and other factors can lead to an inaccurate and incomplete uncertainty evaluation. In this paper, the noise variance is used to represent the noise level of seismic data and the uncertainties from seismic wavelet extraction and noise level estimation are considered in inversion. Assuming that the probability distribution of the noise variance meets the inverse gamma distribution and the seismic wavelet meets the Gaussian distribution, we could obtain the conditional distribution for one variable given another analytically using well-log data and seismic data. In order to integrate the uncertainty from noise level estimation and wavelet extraction into the seismic impedance inversion, the Gibbs sampler algorithm was applied to draw a set of realizations of noise variance and wavelet. For each realization, the corresponding posterior probability model of impedance was achieved by Bayesian linear inversion and the final posterior probability of the impedance model was obtained by integrating all the single posterior probabilities for each pair of wavelet and noise variance. Synthetic and real data experiments showed that the uncertainties of seismic wavelet extraction and noise level estimation have an important influence on inversion results and their uncertainties. The proposed method could effectively integrate the uncertainty of wavelet and noise estimation to obtain a more accurate and comprehensive uncertainty evaluation. Under the assumption that the model meets the linear relationship and the parameters meet some specified distribution, the proposed method has high calculation efficiency. However, it also loses some accuracy when the assumptions are not completely consistent with the actual situation.

An Improved Altimeter in-Orbit Range Noise-Level Estimation Approach Based on Along-Track Differential Method

Satellite radar altimeters are advanced remote sensing devices that play an important role in observing the global marine environment. Accurately estimating the noise level of altimeter in-orbit ranging data is crucial for evaluating the payload performance, analyzing sea conditions, and monitoring data quality. In this study, we propose an approach based on the differential processing of along-track odd–even data sequences for altimeter in-orbit range noise-level estimation. Using the long-term along-track data sequence can notably improve the issue in the existing method in that the noise level is underestimated owing to the utilization of a relatively short data segment. On the basis of an analysis of the influence of low-frequency components on noise-level estimation, the mathematical formulas of the above differential method were deduced, and the efficacy of the approach in assessing the noise level of altimeter in-orbit data was demonstrated by simulation experiments. This method was used to estimate the noise levels of the 20 Hz datasets of Jason-3 and Sentinel-6, and the idea of the time-domain difference was extended to the frequency domain. The statistical results showed that the 20 Hz noise levels at the significant wave height (SWH) = 2 m were 7.41 cm (Jason-3 low-resolution (LR) mode), 6.66 cm (Sentinel-6 LR mode), and 3.13 cm (Sentinel-6 high-resolution (HR) mode). The power spectrum density analysis further verified its accuracy. By reprocessing the 20 Hz data of Sentinel-6 into 10, 5, and 1 Hz, the effectiveness of the along-track odd–even differential method to directly evaluate the noise level of 1 Hz data was explored, and the impact of ocean signals such as swells on noise-level estimation in synthetic aperture mode was discussed.

A semisupervised classification algorithm combining noise learning theory and a disagreement cotraining framework

In the era of big data, the data in many business scenarios are characterized by a small number of labelled samples and a large number of unlabelled samples. It is quite difficult to classify and identify such data and provide effective decision support for a business. A commonly employed processing method in this kind of data scenario is the disagreement-based semisupervised learning method, i.e., exchanging high-confidence samples among multiple models as pseudolabel samples to improve each model’s classification performance. As such pseudolabel samples inevitably contain label noise, they may interfere with the subsequent model learning and damage the robustness of the ensemble model. To solve this problem, a semisupervised classification algorithm based on noise learning theory and a disagreement cotraining framework is proposed. In this model, first, the probably approximately correct (PAC) estimation theory under label noise conditions is applied, the relationship between the label noise level and model robust estimation in the process of multiround cotraining is discussed, and a disagreement elimination algorithm framework based on multiple-model (feature argument and select (FANS) algorithm and L1 penalized logistics regression (PLR) algorithm) cotraining is constructed based on this theoretical relationship. The experimental results show that the algorithm proposed in this paper gives not only a high-confidence sample set that meets the upper bound constraint of the label noise level but also a robust ensemble model capable of resisting sampling bias. The work performed in this paper provides a new research perspective for semisupervised learning theory based on disagreement.

A Single-Image Noise Estimation Algorithm Based on Pixel-Level Low-Rank Low-Texture Patch and Principal Component Analysis.

Noise level is an important parameter for image denoising in many image-processing applications. We propose a noise estimation algorithm based on pixel-level low-rank, low-texture subblocks and principal component analysis for white Gaussian noise. First, an adaptive clustering algorithm, based on a dichotomy merge, adaptive pixel-level low-rank matrix construction method and a gradient covariance low-texture subblock selection method, is proposed to construct a pixel-level low-rank, low-texture subblock matrix. The adaptive clustering algorithm can improve the low-rank property of the constructed matrix and reduce the content of the image information in the eigenvalues of the matrix. Then, an eigenvalue selection method is proposed to eliminate matrix eigenvalues representing the image to avoid an inaccurate estimation of the noise level caused by using the minimum eigenvalue. The experimental results show that, compared with existing state-of-the-art methods, our proposed algorithm has, in most cases, the highest accuracy and robustness of noise level estimation for various scenarios with different noise levels, especially when the noise is high.

Statistical Pass-By for Unattended Road Traffic Noise Measurement in an Urban Environment.

Low-noise surfaces have become a common mitigation action in the last decade, so much so that different methods for feature extraction have been established to evaluate their efficacy. Among these, the Close Proximity Index (CPX) evaluates the noise emissions by means of multiple runs at different speeds performed with a vehicle equipped with a reference tire and with acoustic sensors close to the wheel. However, signals acquired with CPX make it source oriented, and the analysis does not consider the real traffic flow of the studied site for a receiver-oriented approach. These aspects are remedied by Statistical Pass-By (SPB), a method based on sensor feature extraction with live detection of events; noise and speed acquisitions are performed at the roadside in real case scenarios. Unfortunately, the specific SPB requirements for its measurement setup do not allow an evaluation in urban context unless a special setup is used, but this may alter the acoustical context in which the measurement was performed. The present paper illustrates the testing and validation of a method named Urban Pass-By (U-SPB), developed during the LIFE NEREiDE project. U-SPB originates from standard SPB, exploits unattended measurements and develops an in-lab feature detection and extraction procedure. The U-SPB extends the evaluation in terms of before/after data comparison of the efficiency of low-noise laying in an urban context while combining the estimation of long-term noise levels and traffic parameters for other environmental noise purposes, such as noise mapping and action planning.

Blind Additive Gaussian White Noise Level Estimation from a Single Image by Employing Chi-Square Distribution.

The additive Gaussian white noise (AGWN) level in real-life images is usually unknown, for which the empirical setting will make the denoising methods over-smooth fine structures or remove noise incompletely. The previous noise level estimation methods are easily lost in accurately estimating them from images with complicated structures. To cope with this issue, we propose a novel noise level estimation scheme based on Chi-square distribution, including the following key points: First, a degraded image is divided into many image patches through a sliding window. Then, flat patches are selected by using a patch selection strategy on the gradient maps of those image patches. Next, the initial noise level is calculated by employing Chi-square distribution on the selected flat patches. Finally, the stable noise level is optimized by an iterative strategy. Quantitative, with association, to qualitative results of experiments on synthetic real-life images validate that the proposed noise level estimation method is effective and even superior to the state-of-the-art methods. Extensive experiments on noise removal using BM3D further illustrate that the proposed noise level estimation method is more beneficial for achieving favorable denoising performance with detail preservation.

NLM Parameter Optimization for $\varphi$-OTDR Signal

The filtering parameters of non-local means (NLM) that seriously affect the denoising results are usually optimized based on the noise level estimation. But the noise level is unknown in many cases. In this paper, a simple method for optimizing NLM parameters based on autocorrelation function (ACF) is proposed from the perspective of signal estimation, which uses the periodic lag of the autocorrelation function to estimate the vibration signal. This method is verified with a hypothetical clean image corrupted by additive noise, and the NLM parameter optimization results are compared with those obtained by two traditional methods based on peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) respectively. Then it is tested with the practical vibration signal of a phase-sensitive optical time-domain reflectometer ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\varphi$</tex-math></inline-formula> -OTDR). The fidelity and spatial resolution of the denoised practical signal are analyzed. This work helps to improve the performance of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\varphi$</tex-math></inline-formula> -OTDR and signal recognition.

Refinement of Hottopixx Method for Nonnegative Matrix Factorization Under Noisy Separability

Hottopixx, proposed by Bittorf et al. at NIPS 2012, is an algorithm for solving nonnegative matrix factorization (NMF) problems under the separability assumption. Separable NMFs have important applications, such as topic extraction from documents and unmixing of hyperspectral images. In such applications, the robustness of the algorithm to noise is the key to success. Hottopixx has been shown to be robust to noise, and its robustness can be further enhanced through postprocessing. However, there is a drawback. Hottopixx and its postprocessing require us to estimate the noise level involved in the matrix we want to factorize before running, since they use it as part of the input data. The noise-level estimation is not an easy task. In this paper, we overcome this drawback. We present a refinement of Hottopixx and its postprocessing that runs without prior knowledge of the noise level. We show that the refinement has almost the same robustness to noise as the original algorithm.