CNN-Based Projected Gradient Descent for Consistent Image Reconstruction (1709.01809v1)

Abstract: 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.

• The paper introduces a CNN embedded within a PGD framework to enforce measurement consistency in CT image reconstruction.
• It demonstrates superior performance by achieving higher SNR in both noiseless and noisy sparse-view scenarios compared to traditional methods.
• The approach effectively reduces artifacts and radiation dose while requiring minimal training data for improved image quality.

CNN-Based Projected Gradient Descent for Image Reconstruction: A Methodological Overview

The paper presented introduces a novel approach for image reconstruction, particularly focusing on sparse-view computed tomography (CT) in biomedical imaging. The authors propose a convolutional neural network-based projected gradient descent (CNN-PGD) method. This method incorporates a CNN within the projected gradient descent framework to maintain consistency with the measurements, thus offering a promising solution to inverse problems in imaging where traditional methods falter.

Methodological Contributions

The introduced approach is a methodological shift from conventional image reconstruction algorithms, which are typically categorized into classical, iterative, and learning-based algorithms. The classical methods, such as filtered backprojection (FBP), are fast but introduce artifacts in low-measurement and high-noise scenarios. Iterative methods instead integrate data consistency and regularization, yet they often require manual tuning of regularization parameters and convex priors. Learning-based algorithms, particularly those employing CNNs as image-to-image regressors, have demonstrated state-of-the-art performance on inverse imaging problems but lack feedback mechanisms to ensure measurement consistency.

In response to these limitations, the authors propose an innovative CNN-PGD scheme that combines the merits of iterative and learning-based methods while introducing a feedback mechanism. This is achieved by embedding a trained CNN as a non-linear projector within the PGD framework.

Technical Framework and Results

In the proposed framework, the projector in the PGD is replaced by a CNN, which is trained to act as a projector onto a set of desired images. The CNN effectively moves solutions closer to the solution space as defined by sample images. The methodology ensures convergence to a local solution of the specified non-convex problem.

The experimental results are particularly promising in sparse view CT reconstructions for both noiseless and noisy data settings. When compared against the total-variation (TV) approach and state-of-the-art CNN-based techniques, the proposed CNN-PGD framework consistently yields higher reconstruction quality as measured by SNR (signal-to-noise ratio) metrics. For instance, in cases of extreme dosage reduction, the proposed method shows a marked improvement in SNR, indicating enhanced reconstruction quality and reliability over existing techniques.

Theoretical and Practical Implications

From a theoretical standpoint, this approach extends the classical PGD with a CNN, making it applicable to solving inverse problems with a new non-convex paradigm. The use of CNNs trained as projectors is particularly inspired, providing flexibility to learn data-specific priors from training datasets that are not easily captured by hand-crafted regularization terms.

Practically, the implications of this method are significant. In biomedical imaging, where reconstruction quality directly impacts diagnostic outcomes, the proposed approach promises to reduce radiation dose and decrease acquisition times without compromising image clarity. The ability to train the CNN with relatively small datasets, as demonstrated, is critical in medical applications where large annotated datasets are often challenging to acquire.

Future Prospects

This CNN-PGD approach opens several avenues for future exploration. Further research could focus on expanding its application to other inverse problems, such as super-resolution or MRI reconstruction. Additionally, improvements in network architectures or training strategies may further enhance performance and scalability. It may also be beneficial to explore hybrid methods that integrate advanced noise modeling techniques to improve the network’s resilience against diverse noise environments.

In conclusion, this paper presents a robust framework for high-quality image reconstruction using a CNN embedded within a PGD approach. The rigorous theoretical foundations and empirical validations demonstrate its efficacy, marking a significant step toward more reliable and efficient imaging solutions in the biomedical field.