IVMar 20, 2022
VinDr-Mammo: A large-scale benchmark dataset for computer-aided diagnosis in full-field digital mammographyHieu T. Nguyen, Ha Q. Nguyen, Hieu H. Pham et al.
Mammography, or breast X-ray, is the most widely used imaging modality to detect cancer and other breast diseases. Recent studies have shown that deep learning-based computer-assisted detection and diagnosis (CADe or CADx) tools have been developed to support physicians and improve the accuracy of interpreting mammography. However, most published datasets of mammography are either limited on sample size or digitalized from screen-film mammography (SFM), hindering the development of CADe and CADx tools which are developed based on full-field digital mammography (FFDM). To overcome this challenge, we introduce VinDr-Mammo - a new benchmark dataset of FFDM for detecting and diagnosing breast cancer and other diseases in mammography. The dataset consists of 5,000 mammography exams, each of which has four standard views and is double read with disagreement (if any) being resolved by arbitration. It is created for the assessment of Breast Imaging Reporting and Data System (BI-RADS) and density at the breast level. In addition, the dataset also provides the category, location, and BI-RADS assessment of non-benign findings. We make VinDr-Mammo publicly available on PhysioNet as a new imaging resource to promote advances in developing CADe and CADx tools for breast cancer screening.
IVMar 20, 2022
PediCXR: An open, large-scale chest radiograph dataset for interpretation of common thoracic diseases in childrenHieu H. Pham, Ngoc H. Nguyen, Thanh T. Tran et al.
The development of diagnostic models for detecting and diagnosing pediatric diseases in CXR scans is undertaken due to the lack of high-quality physician-annotated datasets. To overcome this challenge, we introduce and release PediCXR, a new pediatric CXR dataset of 9,125 studies retrospectively collected from a major pediatric hospital in Vietnam between 2020 and 2021. Each scan was manually annotated by a pediatric radiologist with more than ten years of experience. The dataset was labeled for the presence of 36 critical findings and 15 diseases. In particular, each abnormal finding was identified via a rectangle bounding box on the image. To the best of our knowledge, this is the first and largest pediatric CXR dataset containing lesion-level annotations and image-level labels for the detection of multiple findings and diseases. For algorithm development, the dataset was divided into a training set of 7,728 and a test set of 1,397. To encourage new advances in pediatric CXR interpretation using data-driven approaches, we provide a detailed description of the PediCXR data sample and make the dataset publicly available on https://physionet.org/content/pedicxr/1.0.0/
CVMar 20, 2022
Learning from Multiple Expert Annotators for Enhancing Anomaly Detection in Medical Image AnalysisKhiem H. Le, Tuan V. Tran, Hieu H. Pham et al.
Building an accurate computer-aided diagnosis system based on data-driven approaches requires a large amount of high-quality labeled data. In medical imaging analysis, multiple expert annotators often produce subjective estimates about "ground truth labels" during the annotation process, depending on their expertise and experience. As a result, the labeled data may contain a variety of human biases with a high rate of disagreement among annotators, which significantly affect the performance of supervised machine learning algorithms. To tackle this challenge, we propose a simple yet effective approach to combine annotations from multiple radiology experts for training a deep learning-based detector that aims to detect abnormalities on medical scans. The proposed method first estimates the ground truth annotations and confidence scores of training examples. The estimated annotations and their scores are then used to train a deep learning detector with a re-weighted loss function to localize abnormal findings. We conduct an extensive experimental evaluation of the proposed approach on both simulated and real-world medical imaging datasets. The experimental results show that our approach significantly outperforms baseline approaches that do not consider the disagreements among annotators, including methods in which all of the noisy annotations are treated equally as ground truth and the ensemble of different models trained on different label sets provided separately by annotators.
IVMar 20, 2022
Phase Recognition in Contrast-Enhanced CT Scans based on Deep Learning and Random SamplingBinh T. Dao, Thang V. Nguyen, Hieu H. Pham et al.
A fully automated system for interpreting abdominal computed tomography (CT) scans with multiple phases of contrast enhancement requires an accurate classification of the phases. This work aims at developing and validating a precise, fast multi-phase classifier to recognize three main types of contrast phases in abdominal CT scans. We propose in this study a novel method that uses a random sampling mechanism on top of deep CNNs for the phase recognition of abdominal CT scans of four different phases: non-contrast, arterial, venous, and others. The CNNs work as a slice-wise phase prediction, while the random sampling selects input slices for the CNN models. Afterward, majority voting synthesizes the slice-wise results of the CNNs, to provide the final prediction at scan level. Our classifier was trained on 271,426 slices from 830 phase-annotated CT scans, and when combined with majority voting on 30% of slices randomly chosen from each scan, achieved a mean F1-score of 92.09% on our internal test set of 358 scans. The proposed method was also evaluated on 2 external test sets: CTPAC-CCRCC (N = 242) and LiTS (N = 131), which were annotated by our experts. Although a drop in performance has been observed, the model performance remained at a high level of accuracy with a mean F1-score of 76.79% and 86.94% on CTPAC-CCRCC and LiTS datasets, respectively. Our experimental results also showed that the proposed method significantly outperformed the state-of-the-art 3D approaches while requiring less computation time for inference.
IVAug 6, 2022
An Accurate and Explainable Deep Learning System Improves Interobserver Agreement in the Interpretation of Chest RadiographHieu H. Pham, Ha Q. Nguyen, Hieu T. Nguyen et al.
Recent artificial intelligence (AI) algorithms have achieved radiologist-level performance on various medical classification tasks. However, only a few studies addressed the localization of abnormal findings from CXR scans, which is essential in explaining the image-level classification to radiologists. We introduce in this paper an explainable deep learning system called VinDr-CXR that can classify a CXR scan into multiple thoracic diseases and, at the same time, localize most types of critical findings on the image. VinDr-CXR was trained on 51,485 CXR scans with radiologist-provided bounding box annotations. It demonstrated a comparable performance to experienced radiologists in classifying 6 common thoracic diseases on a retrospective validation set of 3,000 CXR scans, with a mean area under the receiver operating characteristic curve (AUROC) of 0.967 (95% confidence interval [CI]: 0.958-0.975). The VinDr-CXR was also externally validated in independent patient cohorts and showed its robustness. For the localization task with 14 types of lesions, our free-response receiver operating characteristic (FROC) analysis showed that the VinDr-CXR achieved a sensitivity of 80.2% at the rate of 1.0 false-positive lesion identified per scan. A prospective study was also conducted to measure the clinical impact of the VinDr-CXR in assisting six experienced radiologists. The results indicated that the proposed system, when used as a diagnosis supporting tool, significantly improved the agreement between radiologists themselves with an increase of 1.5% in mean Fleiss' Kappa. We also observed that, after the radiologists consulted VinDr-CXR's suggestions, the agreement between each of them and the system was remarkably increased by 3.3% in mean Cohen's Kappa.
IVSep 11, 2022
Learning to diagnose common thorax diseases on chest radiographs from radiology reports in VietnameseThao T. B. Nguyen, Tam M. Vo, Thang V. Nguyen et al.
We propose a data collecting and annotation pipeline that extracts information from Vietnamese radiology reports to provide accurate labels for chest X-ray (CXR) images. This can benefit Vietnamese radiologists and clinicians by annotating data that closely match their endemic diagnosis categories which may vary from country to country. To assess the efficacy of the proposed labeling technique, we built a CXR dataset containing 9,752 studies and evaluated our pipeline using a subset of this dataset. With an F1-score of at least 0.9923, the evaluation demonstrates that our labeling tool performs precisely and consistently across all classes. After building the dataset, we train deep learning models that leverage knowledge transferred from large public CXR datasets. We employ a variety of loss functions to overcome the curse of imbalanced multi-label datasets and conduct experiments with various model architectures to select the one that delivers the best performance. Our best model (CheXpert-pretrained EfficientNet-B2) yields an F1-score of 0.6989 (95% CI 0.6740, 0.7240), AUC of 0.7912, sensitivity of 0.7064 and specificity of 0.8760 for the abnormal diagnosis in general. Finally, we demonstrate that our coarse classification (based on five specific locations of abnormalities) yields comparable results to fine classification (twelve pathologies) on the benchmark CheXpert dataset for general anomaly detection while delivering better performance in terms of the average performance of all classes.
CVMar 20, 2022
A Novel Transparency Strategy-based Data Augmentation Approach for BI-RADS Classification of MammogramsSam B. Tran, Huyen T. X. Nguyen, Chi Phan et al.
Image augmentation techniques have been widely investigated to improve the performance of deep learning (DL) algorithms on mammography classification tasks. Recent methods have proved the efficiency of image augmentation on data deficiency or data imbalance issues. In this paper, we propose a novel transparency strategy to boost the Breast Imaging Reporting and Data System (BI-RADS) scores of mammogram classifiers. The proposed approach utilizes the Region of Interest (ROI) information to generate more high-risk training examples for breast cancer (BI-RADS 3, 4, 5) from original images. Our extensive experiments on three different datasets show that the proposed approach significantly improves the mammogram classification performance and surpasses a state-of-the-art data augmentation technique called CutMix. This study also highlights that our transparency method is more effective than other augmentation strategies for BI-RADS classification and can be widely applied to other computer vision tasks.
CVAug 5, 2022
Slice-level Detection of Intracranial Hemorrhage on CT Using Deep Descriptors of Adjacent SlicesDat T. Ngo, Thao T. B. Nguyen, Hieu T. Nguyen et al.
The rapid development in representation learning techniques such as deep neural networks and the availability of large-scale, well-annotated medical imaging datasets have to a rapid increase in the use of supervised machine learning in the 3D medical image analysis and diagnosis. In particular, deep convolutional neural networks (D-CNNs) have been key players and were adopted by the medical imaging community to assist clinicians and medical experts in disease diagnosis and treatment. However, training and inferencing deep neural networks such as D-CNN on high-resolution 3D volumes of Computed Tomography (CT) scans for diagnostic tasks pose formidable computational challenges. This challenge raises the need of developing deep learning-based approaches that are robust in learning representations in 2D images, instead 3D scans. In this work, we propose for the first time a new strategy to train \emph{slice-level} classifiers on CT scans based on the descriptors of the adjacent slices along the axis. In particular, each of which is extracted through a convolutional neural network (CNN). This method is applicable to CT datasets with per-slice labels such as the RSNA Intracranial Hemorrhage (ICH) dataset, which aims to predict the presence of ICH and classify it into 5 different sub-types. We obtain a single model in the top 4% best-performing solutions of the RSNA ICH challenge, where model ensembles are allowed. Experiments also show that the proposed method significantly outperforms the baseline model on CQ500. The proposed method is general and can be applied to other 3D medical diagnosis tasks such as MRI imaging. To encourage new advances in the field, we will make our codes and pre-trained model available upon acceptance of the paper.
CVMar 29, 2023
Improving Object Detection in Medical Image Analysis through Multiple Expert Annotators: An Empirical InvestigationHieu H. Pham, Khiem H. Le, Tuan V. Tran et al.
The work discusses the use of machine learning algorithms for anomaly detection in medical image analysis and how the performance of these algorithms depends on the number of annotators and the quality of labels. To address the issue of subjectivity in labeling with a single annotator, we introduce a simple and effective approach that aggregates annotations from multiple annotators with varying levels of expertise. We then aim to improve the efficiency of predictive models in abnormal detection tasks by estimating hidden labels from multiple annotations and using a re-weighted loss function to improve detection performance. Our method is evaluated on a real-world medical imaging dataset and outperforms relevant baselines that do not consider disagreements among annotators.
IVApr 1, 2023
Evaluating the impact of an explainable machine learning system on the interobserver agreement in chest radiograph interpretationHieu H. Pham, Ha Q. Nguyen, Hieu T. Nguyen et al.
We conducted a prospective study to measure the clinical impact of an explainable machine learning system on interobserver agreement in chest radiograph interpretation. The AI system, which we call as it VinDr-CXR when used as a diagnosis-supporting tool, significantly improved the agreement between six radiologists with an increase of 1.5% in mean Fleiss' Kappa. In addition, we also observed that, after the radiologists consulted AI's suggestions, the agreement between each radiologist and the system was remarkably increased by 3.3% in mean Cohen's Kappa. This work has been accepted for publication in IEEE Access and this paper is our short version submitted to the Midwest Machine Learning Symposium (MMLS 2023), Chicago, IL, USA.
CVMay 22, 2020Code
A CNN-LSTM Architecture for Detection of Intracranial Hemorrhage on CT scansNhan T. Nguyen, Dat Q. Tran, Nghia T. Nguyen et al.
We propose a novel method that combines a convolutional neural network (CNN) with a long short-term memory (LSTM) mechanism for accurate prediction of intracranial hemorrhage on computed tomography (CT) scans. The CNN plays the role of a slice-wise feature extractor while the LSTM is responsible for linking the features across slices. The whole architecture is trained end-to-end with input being an RGB-like image formed by stacking 3 different viewing windows of a single slice. We validate the method on the recent RSNA Intracranial Hemorrhage Detection challenge and on the CQ500 dataset. For the RSNA challenge, our best single model achieves a weighted log loss of 0.0522 on the leaderboard, which is comparable to the top 3% performances, almost all of which make use of ensemble learning. Importantly, our method generalizes very well: the model trained on the RSNA dataset significantly outperforms the 2D model, which does not take into account the relationship between slices, on CQ500. Our codes and models is publicly avaiable at https://github.com/VinBDI-MedicalImagingTeam/midl2020-cnnlstm-ich.
IVDec 8, 2021
A novel multi-view deep learning approach for BI-RADS and density assessment of mammogramsHuyen T. X. Nguyen, Sam B. Tran, Dung B. Nguyen et al.
Advanced deep learning (DL) algorithms may predict the patient's risk of developing breast cancer based on the Breast Imaging Reporting and Data System (BI-RADS) and density standards. Recent studies have suggested that the combination of multi-view analysis improved the overall breast exam classification. In this paper, we propose a novel multi-view DL approach for BI-RADS and density assessment of mammograms. The proposed approach first deploys deep convolutional networks for feature extraction on each view separately. The extracted features are then stacked and fed into a Light Gradient Boosting Machine (LightGBM) classifier to predict BI-RADS and density scores. We conduct extensive experiments on both the internal mammography dataset and the public dataset Digital Database for Screening Mammography (DDSM). The experimental results demonstrate that the proposed approach outperforms the single-view classification approach on two benchmark datasets by huge F1-score margins (+5% on the internal dataset and +10% on the DDSM dataset). These results highlight the vital role of combining multi-view information to improve the performance of breast cancer risk prediction.
IVAug 14, 2021
DICOM Imaging Router: An Open Deep Learning Framework for Classification of Body Parts from DICOM X-ray ScansHieu H. Pham, Dung V. Do, Ha Q. Nguyen
X-ray imaging in DICOM format is the most commonly used imaging modality in clinical practice, resulting in vast, non-normalized databases. This leads to an obstacle in deploying AI solutions for analyzing medical images, which often requires identifying the right body part before feeding the image into a specified AI model. This challenge raises the need for an automated and efficient approach to classifying body parts from X-ray scans. Unfortunately, to the best of our knowledge, there is no open tool or framework for this task to date. To fill this lack, we introduce a DICOM Imaging Router that deploys deep CNNs for categorizing unknown DICOM X-ray images into five anatomical groups: abdominal, adult chest, pediatric chest, spine, and others. To this end, a large-scale X-ray dataset consisting of 16,093 images has been collected and manually classified. We then trained a set of state-of-the-art deep CNNs using a training set of 11,263 images. These networks were then evaluated on an independent test set of 2,419 images and showed superior performance in classifying the body parts. Specifically, our best performing model achieved a recall of 0.982 (95% CI, 0.977-0.988), a precision of 0.985 (95% CI, 0.975-0.989) and a F1-score of 0.981 (95% CI, 0.976-0.987), whilst requiring less computation for inference (0.0295 second per image). Our external validity on 1,000 X-ray images shows the robustness of the proposed approach across hospitals. These remarkable performances indicate that deep CNNs can accurately and effectively differentiate human body parts from X-ray scans, thereby providing potential benefits for a wide range of applications in clinical settings. The dataset, codes, and trained deep learning models from this study will be made publicly available on our project website at https://vindr.ai/.
IVAug 14, 2021
Learning to Automatically Diagnose Multiple Diseases in Pediatric Chest Radiographs Using Deep Convolutional Neural NetworksThanh T. Tran, Hieu H. Pham, Thang V. Nguyen et al.
Chest radiograph (CXR) interpretation in pediatric patients is error-prone and requires a high level of understanding of radiologic expertise. Recently, deep convolutional neural networks (D-CNNs) have shown remarkable performance in interpreting CXR in adults. However, there is a lack of evidence indicating that D-CNNs can recognize accurately multiple lung pathologies from pediatric CXR scans. In particular, the development of diagnostic models for the detection of pediatric chest diseases faces significant challenges such as (i) lack of physician-annotated datasets and (ii) class imbalance problems. In this paper, we retrospectively collect a large dataset of 5,017 pediatric CXR scans, for which each is manually labeled by an experienced radiologist for the presence of 10 common pathologies. A D-CNN model is then trained on 3,550 annotated scans to classify multiple pediatric lung pathologies automatically. To address the high-class imbalance issue, we propose to modify and apply "Distribution-Balanced loss" for training D-CNNs which reshapes the standard Binary-Cross Entropy loss (BCE) to efficiently learn harder samples by down-weighting the loss assigned to the majority classes. On an independent test set of 777 studies, the proposed approach yields an area under the receiver operating characteristic (AUC) of 0.709 (95% CI, 0.690-0.729). The sensitivity, specificity, and F1-score at the cutoff value are 0.722 (0.694-0.750), 0.579 (0.563-0.595), and 0.389 (0.373-0.405), respectively. These results significantly outperform previous state-of-the-art methods on most of the target diseases. Moreover, our ablation studies validate the effectiveness of the proposed loss function compared to other standard losses, e.g., BCE and Focal Loss, for this learning task. Overall, we demonstrate the potential of D-CNNs in interpreting pediatric CXRs.
IVJul 3, 2021
VinDr-RibCXR: A Benchmark Dataset for Automatic Segmentation and Labeling of Individual Ribs on Chest X-raysHoang C. Nguyen, Tung T. Le, Hieu H. Pham et al.
We introduce a new benchmark dataset, namely VinDr-RibCXR, for automatic segmentation and labeling of individual ribs from chest X-ray (CXR) scans. The VinDr-RibCXR contains 245 CXRs with corresponding ground truth annotations provided by human experts. A set of state-of-the-art segmentation models are trained on 196 images from the VinDr-RibCXR to segment and label 20 individual ribs. Our best performing model obtains a Dice score of 0.834 (95% CI, 0.810--0.853) on an independent test set of 49 images. Our study, therefore, serves as a proof of concept and baseline performance for future research.
IVJun 24, 2021
VinDr-SpineXR: A deep learning framework for spinal lesions detection and classification from radiographsHieu T. Nguyen, Hieu H. Pham, Nghia T. Nguyen et al.
Radiographs are used as the most important imaging tool for identifying spine anomalies in clinical practice. The evaluation of spinal bone lesions, however, is a challenging task for radiologists. This work aims at developing and evaluating a deep learning-based framework, named VinDr-SpineXR, for the classification and localization of abnormalities from spine X-rays. First, we build a large dataset, comprising 10,468 spine X-ray images from 5,000 studies, each of which is manually annotated by an experienced radiologist with bounding boxes around abnormal findings in 13 categories. Using this dataset, we then train a deep learning classifier to determine whether a spine scan is abnormal and a detector to localize 7 crucial findings amongst the total 13. The VinDr-SpineXR is evaluated on a test set of 2,078 images from 1,000 studies, which is kept separate from the training set. It demonstrates an area under the receiver operating characteristic curve (AUROC) of 88.61% (95% CI 87.19%, 90.02%) for the image-level classification task and a mean average precision (mAP@0.5) of 33.56% for the lesion-level localization task. These results serve as a proof of concept and set a baseline for future research in this direction. To encourage advances, the dataset, codes, and trained deep learning models are made publicly available.
CVMay 25, 2020
Interpreting Chest X-rays via CNNs that Exploit Hierarchical Disease Dependencies and Uncertainty LabelsHieu H. Pham, Tung T. Le, Dat T. Ngo et al.
The chest X-rays (CXRs) is one of the views most commonly ordered by radiologists (NHS),which is critical for diagnosis of many different thoracic diseases. Accurately detecting thepresence of multiple diseases from CXRs is still a challenging task. We present a multi-labelclassification framework based on deep convolutional neural networks (CNNs) for diagnos-ing the presence of 14 common thoracic diseases and observations. Specifically, we trained astrong set of CNNs that exploit dependencies among abnormality labels and used the labelsmoothing regularization (LSR) for a better handling of uncertain samples. Our deep net-works were trained on over 200,000 CXRs of the recently released CheXpert dataset (Irvinandal., 2019) and the final model, which was an ensemble of the best performing networks,achieved a mean area under the curve (AUC) of 0.940 in predicting 5 selected pathologiesfrom the validation set. To the best of our knowledge, this is the highest AUC score yetreported to date. More importantly, the proposed method was also evaluated on an inde-pendent test set of the CheXpert competition, containing 500 CXR studies annotated by apanel of 5 experienced radiologists. The reported performance was on average better than2.6 out of 3 other individual radiologists with a mean AUC of 0.930, which had led to thecurrent state-of-the-art performance on the CheXpert test set.
IVNov 15, 2019
Interpreting chest X-rays via CNNs that exploit hierarchical disease dependencies and uncertainty labelsHieu H. Pham, Tung T. Le, Dat Q. Tran et al.
Chest radiography is one of the most common types of diagnostic radiology exams, which is critical for screening and diagnosis of many different thoracic diseases. Specialized algorithms have been developed to detect several specific pathologies such as lung nodule or lung cancer. However, accurately detecting the presence of multiple diseases from chest X-rays (CXRs) is still a challenging task. This paper presents a supervised multi-label classification framework based on deep convolutional neural networks (CNNs) for predicting the risk of 14 common thoracic diseases. We tackle this problem by training state-of-the-art CNNs that exploit dependencies among abnormality labels. We also propose to use the label smoothing technique for a better handling of uncertain samples, which occupy a significant portion of almost every CXR dataset. Our model is trained on over 200,000 CXRs of the recently released CheXpert dataset and achieves a mean area under the curve (AUC) of 0.940 in predicting 5 selected pathologies from the validation set. This is the highest AUC score yet reported to date. The proposed method is also evaluated on the independent test set of the CheXpert competition, which is composed of 500 CXR studies annotated by a panel of 5 experienced radiologists. The performance is on average better than 2.6 out of 3 other individual radiologists with a mean AUC of 0.930, which ranks first on the CheXpert leaderboard at the time of writing this paper.
CVSep 6, 2017
CNN-Based Projected Gradient Descent for Consistent Image ReconstructionHarshit Gupta, Kyong Hwan Jin, Ha Q. Nguyen et al.
We present a new method for image reconstruction which replaces the projector in a projected gradient descent (PGD) with a convolutional neural network (CNN). CNNs trained as high-dimensional (image-to-image) regressors have recently been used to efficiently solve inverse problems in imaging. However, these approaches lack a feedback mechanism to enforce that the reconstructed image is consistent with the measurements. This is crucial for inverse problems, and more so in biomedical imaging, where the reconstructions are used for diagnosis. In our scheme, the gradient descent enforces measurement consistency, while the CNN recursively projects the solution closer to the space of desired reconstruction images. We provide a formal framework to ensure that the classical PGD converges to a local minimizer of a non-convex constrained least-squares problem. When the projector is replaced with a CNN, we propose a relaxed PGD, which always converges. Finally, we propose a simple scheme to train a CNN to act like a projector. Our experiments on sparse view Computed Tomography (CT) reconstruction for both noiseless and noisy measurements show an improvement over the total-variation (TV) method and a recent CNN-based technique.
LGMay 16, 2017
Learning Convex Regularizers for Optimal Bayesian DenoisingHa Q. Nguyen, Emrah Bostan, Michael Unser
We propose a data-driven algorithm for the maximum a posteriori (MAP) estimation of stochastic processes from noisy observations. The primary statistical properties of the sought signal is specified by the penalty function (i.e., negative logarithm of the prior probability density function). Our alternating direction method of multipliers (ADMM)-based approach translates the estimation task into successive applications of the proximal mapping of the penalty function. Capitalizing on this direct link, we define the proximal operator as a parametric spline curve and optimize the spline coefficients by minimizing the average reconstruction error for a given training set. The key aspects of our learning method are that the associated penalty function is constrained to be convex and the convergence of the ADMM iterations is proven. As a result of these theoretical guarantees, adaptation of the proposed framework to different levels of measurement noise is extremely simple and does not require any retraining. We apply our method to estimation of both sparse and non-sparse models of Lévy processes for which the minimum mean square error (MMSE) estimators are available. We carry out a single training session and perform comparisons at various signal-to-noise ratio (SNR) values. Simulations illustrate that the performance of our algorithm is practically identical to the one of the MMSE estimator irrespective of the noise power.