[Paper Review] Deep Convolutional Framelet Denosing for Low-Dose CT via Wavelet Residual Network

Eun‐Hee Kang, Jaejun Yoo+1 more|arXiv (Cornell University)|Jul 31, 2017

Medical Imaging Techniques and Applications42 references4 citations

TL;DR

This paper proposes a deep convolutional framelet denoising method for low-dose CT using a wavelet residual network (WavResNet) that combines the convergence guarantees of framelet-based denoising with the expressive power of deep learning. By interpreting the network as a multi-layer convolutional framelet, the method enables iterative refinement and achieves superior noise suppression while preserving fine anatomical textures and lesion details, outperforming prior methods including MBIR and FBP in lesion detection and image quality.

ABSTRACT

Model based iterative reconstruction (MBIR) algorithms for low-dose X-ray CT are computationally expensive. To address this problem, we recently proposed a deep convolutional neural network (CNN) for low-dose X-ray CT and won the second place in 2016 AAPM Low-Dose CT Grand Challenge. However, some of the texture were not fully recovered. To address this problem, here we propose a novel framelet-based denoising algorithm using wavelet residual network which synergistically combines the expressive power of deep learning and the performance guarantee from the framelet-based denoising algorithms. The new algorithms were inspired by the recent interpretation of the deep convolutional neural network (CNN) as a cascaded convolution framelet signal representation. Extensive experimental results confirm that the proposed networks have significantly improved performance and preserves the detail texture of the original images.

Motivation & Objective

• To address the limitations of existing deep learning-based low-dose CT denoising methods, which often fail to recover fine textures and treat networks as black boxes.
• To integrate the theoretical convergence properties of framelet-based denoising with the representation power of deep neural networks.
• To provide a mathematically interpretable deep learning architecture by linking it to convolutional framelets with ReLU nonlinearities.
• To improve lesion detection and image quality in low-dose CT by enabling iterative refinement through a non-expansive operator framework.
• To demonstrate that the network can be optimized for specific restoration tasks by selecting optimal framelet representations.

Proposed method

• The method interprets a deep convolutional neural network as a multi-layer realization of convolutional framelets with ReLU activation, grounding the network in a well-established mathematical framework.
• A wavelet residual network (WavResNet) is employed to enhance directional feature learning and improve texture recovery in low-dose CT images.
• The network is structured as a feed-forward architecture and an RNN-like iterative version, both derived from the framelet denoising framework.
• The iterative process is modeled as a Krasnoselski-Mann (KM) algorithm, ensuring convergence under non-expansive operator conditions.
• The Jacobian of the network is bounded due to finite convolution filters and ReLU, enabling theoretical convergence proof via non-expansiveness.
• The method uses a redundant global transform and concatenation layers to boost signal recovery and preserve high-frequency details.

Experimental results

Research questions

• RQ1 Can deep learning-based denoising in low-dose CT be theoretically grounded using the convolutional framelet framework?
• RQ2 Does integrating framelet-based iterative refinement into a deep network improve texture and lesion preservation compared to standard CNNs?
• RQ3 Can the network be interpreted as a non-expansive operator to guarantee convergence during iterative denoising?
• RQ4 How does the proposed WavResNet-based framelet network compare to MBIR and FBP in clinical image quality and lesion detection?
• RQ5 Can the network be optimized for specific restoration tasks by selecting appropriate framelet representations?

Key findings

• The proposed method achieved a lesion detection rate of 73% on low-dose CT scans, significantly outperforming FBP (57%) and MBIR (62%) with a p-value of 0.0412 for FBP comparison.
• The network preserved fine anatomical textures and structural details better than prior deep learning methods, as confirmed by visual and quantitative evaluation.
• Theoretical analysis proved that the iterative network is non-expansive and converges under the Krasnoselski-Mann algorithm, ensuring stable optimization.
• The WavResNet-based architecture effectively recovered directional features and reduced streaking artifacts in low-dose CT images.
• The method outperformed the second-place solution in the 2016 AAPM Low-Dose CT Grand Challenge, particularly in texture recovery and lesion visibility.
• Extensive experiments confirmed that the network maintains lesion information while suppressing noise, demonstrating clinical relevance.