Leveraging Deep Stein’s Unbiased Risk Estimator for Unsupervised Xray Denoising
Abstract
Among the plethora of techniques devised to curb the prevalence of noise in medical images, deep learning based approaches have shown the most promise. However, one critical limitation of these deep learning based denoisers is the requirement of highquality noiseless ground truth images that are difficult to obtain in many medical imaging applications such as Xrays. To circumvent this issue, we leverage recently proposed approach of (soltanayev2018training, ) that incorporates Stein’s Unbiased Risk Estimator (SURE) to train a deep convolutional neural network without requiring denoised ground truth Xray data. Our experimental results demonstrate the effectiveness of SURE based approach for denoising Xray images.
Leveraging Deep Stein’s Unbiased Risk Estimator for Unsupervised Xray Denoising
Fahad Shamshad, Muhammad Awais, Muhammad Asim, Zain ul Aabidin Lodhi, Muhammad Umair, Ali Ahmed Department of Electrical Engineering, Information Technology University, Lahore, Pakistan Department of Civil Engineering, University of Toronto, Canada
noticebox[b]Machine Learning for Health (ML4H) Workshop at NeurIPS 2018.\end@float
1 Introduction
Xray images provide crucial support for diagnosis and decision making in many diverse clinical applications. However, Xray images may be corrupted by statistical noise, thus seriously deteriorating the quality and raising the difficulty of diagnosis (thanhreview, ). Therefore, Xray denoising is an essential preprocessing step for improving the quality of raw Xray images and their relevant clinical information content.
Deep learning with massive amounts of training data has revolutionized many image processing and computer vision tasks including image denoising (lecun2015deep, ). Deep learning based denoisers have been recently shown to produce state of the art results (zhang2017beyond, ), and have been extensively investigated for denoising Xray images for enhanced diagnosis reliability (gondara2016medical, ; chen2017low, ). These deep learning based denoisers are usually trained by minimizing mean squared error (MSE). This requires access to abundant high quality and clean ground truth Xray images that are hard to acquire.
In this work, we leverage recently proposed approach of (soltanayev2018training, ) to train a deep convolutional neural network for denoising, using only noisy Xray data. Denoising approach of (soltanayev2018training, ) is based on the classical idea of Stein’s Unbiased Risk Estimator (SURE) (stein1981estimation, ). SURE gives an unbiased estimate of MSE, however, it does not require ground truth data for tuning parameters of denoising algorithm thus circumventing the main hurdle for deep learning based denoisers that require clean ground truth for training.
2 Methodology
We consider recovering true Xray image from its noisy measurements of the form
(1) 
where is noise corrupted image, denotes independent and identically distributed Gaussian noise i.e. where is identity matrix and is standard deviation that is assumed to be known. We are interested in a weakly differentiable function parametrized by that maps noisy Xray images to clean ones . We model by a convolutional neural network (CNN) where are weights of this network. CNN based denoising methods are typically trained by taking a representative set of clean ground truth images along with corresponding set of noise corrupted observations . The network then learns the mapping from noisy observations to clean images by minimizing a supervised loss function; typically mean squared error (MSE). MSE minimizes the error between true images and the network output as follows:
(2) 
Note the dependence of MSE on ground truth clean images . Instead of minimizing MSE, we employ SURE loss that optimizes neural network parameters by minimizing
(3) 
where denotes divergence and is defined as
(4) 
The first term in (3), minimizes the error between observations and corresponding estimates at network output . The second term penalizes neural network based denoiser for varying as its input image is changed. Calculating divergence of the denoiser is a central challenge for SURE based estimators. We estimate divergence via fast Monte Carlo approximation, see (ramani2008monte, ) for details. In short, instead of utilizing a supervised loss of MSE in (2), we optimize network weights in an unsupervised manner using (3), that does not require ground truth; see Figure 1. We leverage the autodifferentiation function of Tensorflow (abadi2016tensorflow, ) to calculate the gradient of the SURE base loss function, that is hard to compute otherwise.
3 Experiments
To evaluate the proposed denoising approach, we use Indiana University’s Chest Xray database (IndianaXrays, ). The database consists of chest Xray images of varying sizes, out of which we select images for training due to the scarcity of computational resources. Training images are rescaled, cropped, and flipped, to form a set of overlapping patches each of size . We use an endtoend trainable denoising convolutional neural network (DnCNN) (zhang2017beyond, ) that have recently shown promising denoising results. DnCNN consists of 16 sequential convolutional layers with residual connections. Training was conducted on batches of size 64 using Adam optimizer for 50 epochs with learning rate set to which was reduced to after 25 epochs. DnCNN was trained using SURE loss, without any ground truth clean data. We perform experiments for three different additive Gaussian noise levels having standard deviations of , and ; see Figure 2 for SURE training loss curve for each noise level. The network easily converges for low noise while higher noise levels make convergence harder. For a benchmark, we also trained DnCNN using MSE loss of (2) and compare its performance with the SURE approach.
For evaluation, we randomly select images from the test set of Indiana University XRay dataset. To quantitatively evaluate the performance of proposed SURE based approach, we use two widely used performance metrics, Peak Signal to Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) (wang2004image, ). PSNR of reconstructed image from true image is defined as for image pixels in the range of 0 and 255. On the other hand, SSIM measure perceived similarity between reconstructed and true image.In addition to Indiana University dataset, we also use images from famous Chest XRays dataset (wang2017chestx, ) for testing as well. Table 1 shows quantitative results for both datasets at different noise levels. Figure 3 shows visual results for both datasets for Gaussian noise having a standard deviation of 25. Quantitative and qualitative results show that model trained on Indiana University dataset also has very compelling results on Chest XRay data. This demonstrates the generalizability of SURE based approach to other datasets of similar modalities. Table 2 shows quantitative comparison between DnCNN trained using SURE loss and MSE loss. Note that although SURE does not require any clean ground truth images, it’s performance is still comparable to DnCNN trained via supervised MSE loss, which requires ground truth images during training.
Dataset 








10  37.50  0.959  9.12  0.06  
25  32.00  0.881  13.15  0.06  
50  27.78  0.763  21.50  0.06  
Chest XRays  10  37.55  0.962  13.57  0.19  
25  31.85  0.877  26.14  0.19  
50  28.88  0.774  45.43  0.19 
Method 






DnCNNSURE  25  32.00  0.88  13.15  
50  27.78  0.76  21.50  
DnCNNMSE  25  35.39  0.95  08.96  
50  29.61  0.82  17.32 
4 Discussion and Future Direction
The main contribution of this work is to demonstrate the effectiveness of SURE for unsupervised Xray denoising. Not only are we able to remove additive noise from Xray images but also preserve the fine structure in Xray scans. Our work assumes that true image is corrupted by Gaussian noise with known variance. In our future work, we will extend this SURE based approach to Poisson noise that is more relevant for Xray imaging, especially in low dose regime. For this, we can use transforms to first convert Poisson noise to Gaussian noise and then use Gaussian noise removal methods. This is because algorithms proposed for Gaussian noise fails to give plausible results on Poisson noise.
Acknowledgement
We gratefully acknowledge the support of the NVIDIA Corporation for the donation of NVIDIA TITAN Xp GPU for our research.
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