Image reconstruction by domain transform manifold learning (1704.08841v1)

Abstract: Image reconstruction plays a critical role in the implementation of all contemporary imaging modalities across the physical and life sciences including optical, MRI, CT, PET, and radio astronomy. During an image acquisition, the sensor encodes an intermediate representation of an object in the sensor domain, which is subsequently reconstructed into an image by an inversion of the encoding function. Image reconstruction is challenging because analytic knowledge of the inverse transform may not exist a priori, especially in the presence of sensor non-idealities and noise. Thus, the standard reconstruction approach involves approximating the inverse function with multiple ad hoc stages in a signal processing chain whose composition depends on the details of each acquisition strategy, and often requires expert parameter tuning to optimize reconstruction performance. We present here a unified framework for image reconstruction, AUtomated TransfOrm by Manifold APproximation (AUTOMAP), which recasts image reconstruction as a data-driven, supervised learning task that allows a mapping between sensor and image domain to emerge from an appropriate corpus of training data. We implement AUTOMAP with a deep neural network and exhibit its flexibility in learning reconstruction transforms for a variety of MRI acquisition strategies, using the same network architecture and hyperparameters. We further demonstrate its efficiency in sparsely representing transforms along low-dimensional manifolds, resulting in superior immunity to noise and reconstruction artifacts compared with conventional handcrafted reconstruction methods. In addition to improving the reconstruction performance of existing acquisition methodologies, we anticipate accelerating the discovery of new acquisition strategies across modalities as the burden of reconstruction becomes lifted by AUTOMAP and learned-reconstruction approaches.

• The paper introduces AUTOMAP, a method that directly maps sensor data to images using deep learning, bypassing complex traditional transforms.
• It demonstrates superior noise immunity and significant artifact reduction compared to conventional methods across multiple MRI acquisition strategies.
• The approach offers a unified framework adaptable to diverse imaging modalities, potentially accelerating low-dose and rapid imaging applications.

Image Reconstruction by Domain Transform Manifold Learning: A Comprehensive Analysis

The paper "Image reconstruction by domain transform manifold learning" by Bo Zhu, Jeremiah Z. Liu, Bruce R. Rosen, and Matthew S. Rosen, presents a novel image reconstruction approach using Automated Transform by Manifold Approximation (AUTOMAP). This approach leverages deep neural networks to enable direct learning of the relationship between sensor data and image domain, offering a unified framework adaptable to various imaging modalities.

Overview

Image reconstruction is pivotal across numerous fields, including optical imaging, MRI, CT, PET, ultrasound, and radio astronomy. Traditional reconstruction methods often rely on multi-stage signal processing chains, which are highly specialized for different acquisition strategies. These methods frequently demand expert-driven parameter tuning, and can struggle amid sensor non-idealities and noise. AUTOMAP aims to circumvent these limitations by repositioning image reconstruction as a supervised learning task.

Methodology

AUTOMAP employs a feed-forward deep neural network that includes fully connected layers followed by a sparse convolutional autoencoder. The neural network maps sensor domain data directly to images, learning a low-dimensional joint manifold to capture relevant features. This eliminates the need for intricate mathematical transforms or iterative optimization methods typically used in conventional approaches.

The presented neural network structure comprises:

• Fully Connected Layers (FC1 to FC3) for projecting sensor data to initial image representation
• Convolutional Layers for refining image features and ensuring sparse representation

Empirical Evaluation

The performance of AUTOMAP was tested across four diverse MRI acquisition strategies:

1. Radon Projection Imaging: Compared against Kaczmarz-Iterative Algebraic Reconstruction Technique (ART).
2. Spiral-Trajectory k-Space: Benchmarked against Conjugate-Gradient SENSE using NUFFT regridding.
3. Poisson-Disc Undersampled k-Space: Evaluated against compressed sensing with wavelet sparsifying transform.
4. Misaligned k-Space: Measured against traditional inverse FFT.

Key findings included:

• Noise Immunity: AUTOMAP demonstrates superior noise resilience, outperforming conventional methods in noisy conditions. Noteworthy is that this resilience emerges intrinsically from the manifold learning process, as noise was not explicitly modeled during training.
• Artifact Reduction: Conventional methods showed various artifacts under noisy conditions, such as aliasing and ringing, which were significantly reduced or absent in AUTOMAP reconstructions.

Theoretical and Practical Implications

Theoretically, AUTOMAP's robust performance challenges conventional reconstruction paradigms by demonstrating the effectiveness of manifold learning in capturing complex transformations. Practically, its application could significantly enhance imaging quality and speed in low-SNR environments, which is crucial for low-dose CT, rapid MRI, and other modalities requiring high-speed or low-intensity acquisitions.

Future developments in AI may focus on refining such manifold approximations, enhancing generalization across even broader modalities and potentially inspiring new acquisition strategies. Given its reliance on real-world data for training, AUTOMAP also fosters advancements in data-driven image processing approaches.

Conclusion

AUTOMAP represents a significant advancement in image reconstruction methodologies, facilitating high-fidelity reconstructions across diverse imaging modalities. Its approach reduces reliance on handcrafted processing chains and promises enhanced robustness to noise and artifacts. As such, AUTOMAP offers a powerful tool for the advancement of both current and emergent imaging techniques.