Complex-Valued CNNs for Medical Image Denoising | by Shubhankar Rawat | Oct, 2022
A novel approach for denoising medical images
Deep learning, especially Convolutional Neural Networks (CNNs), is shaping the future of data-driven problem solving. From text-related problems like speech generation, content writing, etc to vision tasks like image classification, object detection, CNNs are widely used. In the past few years, numerous advanced CNN architectures have been proposed like Graph CNNs, Attention-based CNNs, Complex-valued CNNs etc. In this article I will be summarizing my research paper published here, wherein a novel complex-valued CNN-based deep learning model is proposed for medical image denoising.
INTRODUCTION
Medical imaging has revolutionized the health sector by assisting medical professionals in several ways, including disease diagnosis, treatment, and risk prediction. However, medical images like X-ray, Computed Tomography (CT), ultrasound, and Magnetic Resonance Imaging (MRI) are susceptible to various kinds of noise. For instance, Chest X-Ray (CXR) images are often corrupted by Gaussian noise, which occurs during acquisition, storage, transmission, and processing. Noise in medical images deteriorates the image quality and even makes them diagnostically unusable. This may discourage further decision-making, leading to poor diagnosis, treatment, or analysis of the disease. Therefore, there is always a dire need to reduce the noise from the medical images without harming the potential information as the resulting diagnostics directly impact human health and lives.
Some of the conventional Medical Image Denoising (MID) techniques include basic digital image filters, adaptive filters, non-local means algorithm, and multi-scale techniques. However, the complicated noise in the medical images results in the unsatisfactory performance of these techniques. “Then comes the Convolutional Neural Networks (CNNs)”. Without a doubt, CNNs have been dominating as a solution for numerous data-driven tasks, especially image processing. For MID, various CNN-based architectures like convolutional autoencoders and Generative Adversarial Networks (GANs) have been reported. These CNN techniques involve two CNN architectures, for instance, in GANs we have a generator and discriminator and in autoencoders, we have an encoder and decoder. However, there are numerous methods that involve only one CNN architecture like DnCNN.
Given the CNN-based approaches for MID, one can conclude that all these methods involve real-valued CNNs, i.e., CNN architectures dealing with real numbers. This motivated me to develop CVCNNs for MID and as you may have guessed, this is the first research paper that implements CVCNNs for MID (also, this happens to be my first research paper as well).
Recently, Complex-Valued CNNs (CVCNNs)have gained popularity since they provide better results than their real-valued counterparts, and thanks to the advancements in the hardware industry, the implementation of these models have become possible. Now the following questions arise:
- How are CVCNNs better than their real-valued counterparts
- How can CVCNNs be used for MID
I will not be majorly focusing on the first question since it is beyond the scope of this article however, I may write another article stating the advantages of CVCNNs over their real-valued counterparts, so stay tuned 🙂
THE PROPOSED APPROACH
The proposed CVCNN model for MID is termed as CVMIDNet. The model framework is shown in Fig. 1 where, Conv, BN, and ReLU represent the convolutional layer, batch normalization, and rectified linear unit function.
Following are the main components of the model:
Complex-Valued Convolutional Layer (CVCL)
In a CVCL the real-valued convolutional operation is generalized to complex domain. In a real-valued convolutional layer, a convolution operation is carried out between the input matrix I and a real-valued kernel K, i.e., I*K. In the complex-valued convolutional layer, both I and K are complex matrices such that:
I = Ir + iIc
K = Kr + iKc
where, Ir, Ic, Kr, and Kc are real matrices. Now the complex-valued convolution operation becomes:
I*K = (Ir*Kr − Ic*Kc) + i(Ic*Kr + Ir*Kc)
Complex-valued Batch Normalization (CVBN)
Similar to CVCL, in CVBN the real-valued BN operation is generalized to complex domain in the following manner:
CNB(Z) = BN(A) + i(BN(B))
where BN() and CNB() represent the real-valued and complex-valued BN operation, respectively. Z is a complex-valued parameter considered as Z = A + iB
Complex-valued ReLU (CVReLU)
When it comes to generalizing the real-valued activation function (in this case ReLU), we have numerous ways of doing it and therefore we have different versions of CVReLU. The most common ones include ModReLU, zReLU, and CReLU. In literature, there is enough evidence stating the superior performance of CReLU over other potential counterparts especially for image-related tasks and therefore it was considered for CVMIDNet. CReLU is obtained as follows:
CReLU(z) = ReLU(R(z)) + i(ReLU(I(z)))
Where, z, R(z), and I(z) represent the complex-valued parameter, real part of z, and Imaginary part of z.
DATASET AND EXPERIMENTATION DETAILS
A publicly available CXR images dataset (link) was considered in this research wherein the images were affected by Gaussian noise. CXR images were considered for denoising as they are one of the most significant types of medical imaging techniques due to their cost-effectiveness and non-invasive method. There were 400 images selected for training and 100 (non-overlapping with the training set) images for the test set.
The codes for the whole work were developed in Python using Tensorflow. Custom layers and data generators were also developed wherever necessary.
RESULTS
Peak Signal-to-Noise ratio (PSNR) and Structural similarity index measure (SSIM) were considered for evaluating CVMIDNet. Further, the model was compared with other state-of-the-art MID techniques like BM3D, DnCNN, FDCNN, etc. A real-valued counterpart of CVMIDNet (developed by replacing the complex-valued operations in CVMIDNet with their real-valued counterparts), termed as RVMIDNet was also considered for performance evaluation.
Numerous Gaussian noise levels were considered namely, sigma = 15, 25, 40, 50, and 60 (sigma represents the noise level in Gaussian noise, more here). The results are shown in the tables and figures below.
Upon comparison with other state-of-the-art techniques, it was found that CVMIDNet outperforms all other methods for denoising Gaussian noise affected CXR images for various noise levels.
CONCLUSION
For the first time, CVMIDNet, a novel complex-valued CNN-based deep learning model with residual learning for medical image denoising, has been proposed and implemented. CVMIDNet was implemented using a complex-valued convolutional layer, complex-valued batch normalization, and CReLU activation to remove Gaussian noise from chest X-ray images. Denoising performance of CVMIDNet was compared with four potential state-of-the-art denoising methods, namely, Block-Matching and 3D filtering, DnCNN, Feature-guided Denoising Convolutional Neural Network, and a deep CNN model with residual learning in addition to the RVMIDNet, where RVMIDNet had the same architecture as that of CVMIDNet, but all the operations were real-valued. It was observed that CVMIDNet outperformed all the other models with a significant margin at all the investigated five noise levels. Further, the visual assessment also clearly indicated that CVMIDNet reduced the noise and restored the images more effectively than other compared models.
ENDING NOTES
So this was a brief about my research on a novel approach which got accepted in the journal: Biomedical Signal Processing and Control.
If this article was useful for you then you may find my other articles equally intriguing. Further, if you want or are looking for developing such models then you can contact me at FIVERR: https://www.fiverr.com/shubhankarrawat
HAPPY LEARNING!!
A novel approach for denoising medical images
Deep learning, especially Convolutional Neural Networks (CNNs), is shaping the future of data-driven problem solving. From text-related problems like speech generation, content writing, etc to vision tasks like image classification, object detection, CNNs are widely used. In the past few years, numerous advanced CNN architectures have been proposed like Graph CNNs, Attention-based CNNs, Complex-valued CNNs etc. In this article I will be summarizing my research paper published here, wherein a novel complex-valued CNN-based deep learning model is proposed for medical image denoising.
INTRODUCTION
Medical imaging has revolutionized the health sector by assisting medical professionals in several ways, including disease diagnosis, treatment, and risk prediction. However, medical images like X-ray, Computed Tomography (CT), ultrasound, and Magnetic Resonance Imaging (MRI) are susceptible to various kinds of noise. For instance, Chest X-Ray (CXR) images are often corrupted by Gaussian noise, which occurs during acquisition, storage, transmission, and processing. Noise in medical images deteriorates the image quality and even makes them diagnostically unusable. This may discourage further decision-making, leading to poor diagnosis, treatment, or analysis of the disease. Therefore, there is always a dire need to reduce the noise from the medical images without harming the potential information as the resulting diagnostics directly impact human health and lives.
Some of the conventional Medical Image Denoising (MID) techniques include basic digital image filters, adaptive filters, non-local means algorithm, and multi-scale techniques. However, the complicated noise in the medical images results in the unsatisfactory performance of these techniques. “Then comes the Convolutional Neural Networks (CNNs)”. Without a doubt, CNNs have been dominating as a solution for numerous data-driven tasks, especially image processing. For MID, various CNN-based architectures like convolutional autoencoders and Generative Adversarial Networks (GANs) have been reported. These CNN techniques involve two CNN architectures, for instance, in GANs we have a generator and discriminator and in autoencoders, we have an encoder and decoder. However, there are numerous methods that involve only one CNN architecture like DnCNN.
Given the CNN-based approaches for MID, one can conclude that all these methods involve real-valued CNNs, i.e., CNN architectures dealing with real numbers. This motivated me to develop CVCNNs for MID and as you may have guessed, this is the first research paper that implements CVCNNs for MID (also, this happens to be my first research paper as well).
Recently, Complex-Valued CNNs (CVCNNs)have gained popularity since they provide better results than their real-valued counterparts, and thanks to the advancements in the hardware industry, the implementation of these models have become possible. Now the following questions arise:
- How are CVCNNs better than their real-valued counterparts
- How can CVCNNs be used for MID
I will not be majorly focusing on the first question since it is beyond the scope of this article however, I may write another article stating the advantages of CVCNNs over their real-valued counterparts, so stay tuned 🙂
THE PROPOSED APPROACH
The proposed CVCNN model for MID is termed as CVMIDNet. The model framework is shown in Fig. 1 where, Conv, BN, and ReLU represent the convolutional layer, batch normalization, and rectified linear unit function.
Following are the main components of the model:
Complex-Valued Convolutional Layer (CVCL)
In a CVCL the real-valued convolutional operation is generalized to complex domain. In a real-valued convolutional layer, a convolution operation is carried out between the input matrix I and a real-valued kernel K, i.e., I*K. In the complex-valued convolutional layer, both I and K are complex matrices such that:
I = Ir + iIc
K = Kr + iKc
where, Ir, Ic, Kr, and Kc are real matrices. Now the complex-valued convolution operation becomes:
I*K = (Ir*Kr − Ic*Kc) + i(Ic*Kr + Ir*Kc)
Complex-valued Batch Normalization (CVBN)
Similar to CVCL, in CVBN the real-valued BN operation is generalized to complex domain in the following manner:
CNB(Z) = BN(A) + i(BN(B))
where BN() and CNB() represent the real-valued and complex-valued BN operation, respectively. Z is a complex-valued parameter considered as Z = A + iB
Complex-valued ReLU (CVReLU)
When it comes to generalizing the real-valued activation function (in this case ReLU), we have numerous ways of doing it and therefore we have different versions of CVReLU. The most common ones include ModReLU, zReLU, and CReLU. In literature, there is enough evidence stating the superior performance of CReLU over other potential counterparts especially for image-related tasks and therefore it was considered for CVMIDNet. CReLU is obtained as follows:
CReLU(z) = ReLU(R(z)) + i(ReLU(I(z)))
Where, z, R(z), and I(z) represent the complex-valued parameter, real part of z, and Imaginary part of z.
DATASET AND EXPERIMENTATION DETAILS
A publicly available CXR images dataset (link) was considered in this research wherein the images were affected by Gaussian noise. CXR images were considered for denoising as they are one of the most significant types of medical imaging techniques due to their cost-effectiveness and non-invasive method. There were 400 images selected for training and 100 (non-overlapping with the training set) images for the test set.
The codes for the whole work were developed in Python using Tensorflow. Custom layers and data generators were also developed wherever necessary.
RESULTS
Peak Signal-to-Noise ratio (PSNR) and Structural similarity index measure (SSIM) were considered for evaluating CVMIDNet. Further, the model was compared with other state-of-the-art MID techniques like BM3D, DnCNN, FDCNN, etc. A real-valued counterpart of CVMIDNet (developed by replacing the complex-valued operations in CVMIDNet with their real-valued counterparts), termed as RVMIDNet was also considered for performance evaluation.
Numerous Gaussian noise levels were considered namely, sigma = 15, 25, 40, 50, and 60 (sigma represents the noise level in Gaussian noise, more here). The results are shown in the tables and figures below.
Upon comparison with other state-of-the-art techniques, it was found that CVMIDNet outperforms all other methods for denoising Gaussian noise affected CXR images for various noise levels.
CONCLUSION
For the first time, CVMIDNet, a novel complex-valued CNN-based deep learning model with residual learning for medical image denoising, has been proposed and implemented. CVMIDNet was implemented using a complex-valued convolutional layer, complex-valued batch normalization, and CReLU activation to remove Gaussian noise from chest X-ray images. Denoising performance of CVMIDNet was compared with four potential state-of-the-art denoising methods, namely, Block-Matching and 3D filtering, DnCNN, Feature-guided Denoising Convolutional Neural Network, and a deep CNN model with residual learning in addition to the RVMIDNet, where RVMIDNet had the same architecture as that of CVMIDNet, but all the operations were real-valued. It was observed that CVMIDNet outperformed all the other models with a significant margin at all the investigated five noise levels. Further, the visual assessment also clearly indicated that CVMIDNet reduced the noise and restored the images more effectively than other compared models.
ENDING NOTES
So this was a brief about my research on a novel approach which got accepted in the journal: Biomedical Signal Processing and Control.
If this article was useful for you then you may find my other articles equally intriguing. Further, if you want or are looking for developing such models then you can contact me at FIVERR: https://www.fiverr.com/shubhankarrawat
HAPPY LEARNING!!
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