[Paper Review] CoIL: Coordinate-based Internal Learning for Imaging Inverse Problems

Yu Sun, Jiaming Liu+3 more|arXiv (Cornell University)|Feb 9, 2021

Medical Imaging Techniques and Applications96 references18 citations

TL;DR

CoIL proposes a self-supervised deep learning method that uses a multilayer perceptron (MLP) to learn a continuous representation of the full measurement field in imaging inverse problems by mapping coordinate inputs (e.g., view angle and detector position) to sensor responses. By training solely on the test object’s own sparse, noisy measurements, CoIL generates high-fidelity, full-view sinograms that significantly improve reconstruction quality across diverse methods, including model-based and deep learning-based approaches in sparse-view CT.

ABSTRACT

We propose Coordinate-based Internal Learning (CoIL) as a new deep-learning (DL) methodology for the continuous representation of measurements. Unlike traditional DL methods that learn a mapping from the measurements to the desired image, CoIL trains a multilayer perceptron (MLP) to encode the complete measurement field by mapping the coordinates of the measurements to their responses. CoIL is a self-supervised method that requires no training examples besides the measurements of the test object itself. Once the MLP is trained, CoIL generates new measurements that can be used within a majority of image reconstruction methods. We validate CoIL on sparse-view computed tomography using several widely-used reconstruction methods, including purely model-based methods and those based on DL. Our results demonstrate the ability of CoIL to consistently improve the performance of all the considered methods by providing high-fidelity measurement fields.

Motivation & Objective

• To develop a self-supervised deep learning method that leverages internal redundancy in a single object’s measurements for high-fidelity measurement field reconstruction.
• To eliminate the need for external training datasets by training solely on the test object’s own sparse and noisy measurements.
• To enable synergistic integration with a wide range of image reconstruction methods, including model-based and deep learning-based techniques.
• To demonstrate that coordinate-based neural representation can effectively model and enhance imaging inverse problems in computed tomography.

Proposed method

• A multilayer perceptron (MLP) is trained to map measurement coordinates (e.g., view angle θ and detector location l) to sensor responses r, forming a continuous representation of the full measurement field.
• The MLP is trained using coordinate-response pairs extracted from the actual measurements of the test object, making the method self-supervised and data-efficient.
• The method uses a novel MLP architecture with only 256 hidden neurons, enabling efficient training and deployment despite its compact size.
• The trained MLP generates high-resolution, full-view sinograms by querying the network at any coordinate, which can be used as input to standard reconstruction algorithms.
• The approach is compatible with both model-based methods (e.g., FBP, FISTA-TV) and deep learning-based methods (e.g., FBP-UNet, GM-RED) by providing enhanced measurement inputs.
• A linear expansion-based FFM layer is used to stabilize training and improve the quality of the learned measurement field.

Experimental results

Research questions

• RQ1 Can a coordinate-based neural representation learn a high-fidelity continuous measurement field from only the test object’s own sparse and noisy measurements?
• RQ2 How does the quality of the reconstructed measurement field vary with the number of views and noise levels in the input data?
• RQ3 To what extent can the generated measurement field improve image reconstruction performance across diverse reconstruction algorithms?
• RQ4 Can the proposed method consistently enhance performance in both model-based and deep learning-based reconstruction frameworks?

Key findings

• CoIL-generated sinograms consistently achieve higher SNR than the input measurements, with improvements exceeding 7 dB even at 30 dB input SNR across all view counts.
• For FBP with 60 views and 30 dB input SNR, CoIL improved reconstruction SNR by up to 20 dB, demonstrating substantial performance gains under high noise.
• Even at low noise (50 dB input SNR), CoIL provided measurable improvements: FBP-UNet achieved a 1.02 dB SNR gain when using CoIL-generated measurements.
• Visual comparisons show clear improvements in image quality, with enhanced structural details and reduced artifacts, especially in regions highlighted by arrows in bounding boxes.
• The method synergistically enhanced all tested reconstruction algorithms—model-based (e.g., FBP, FISTA-TV) and deep learning-based (e.g., FBP-UNet, GM-RED)—demonstrating broad compatibility and effectiveness.
• The quality of the CoIL-generated measurement field improves with more views or lower noise, indicating scalability and robustness to input conditions.