Image Reconstruction: From Sparsity to Data-adaptive Methods and Machine Learning (1904.02816v3)

Abstract: The field of medical image reconstruction has seen roughly four types of methods. The first type tended to be analytical methods, such as filtered back-projection (FBP) for X-ray computed tomography (CT) and the inverse Fourier transform for magnetic resonance imaging (MRI), based on simple mathematical models for the imaging systems. These methods are typically fast, but have suboptimal properties such as poor resolution-noise trade-off for CT. A second type is iterative reconstruction methods based on more complete models for the imaging system physics and, where appropriate, models for the sensor statistics. These iterative methods improved image quality by reducing noise and artifacts. The FDA-approved methods among these have been based on relatively simple regularization models. A third type of methods has been designed to accommodate modified data acquisition methods, such as reduced sampling in MRI and CT to reduce scan time or radiation dose. These methods typically involve mathematical image models involving assumptions such as sparsity or low-rank. A fourth type of methods replaces mathematically designed models of signals and systems with data-driven or adaptive models inspired by the field of machine learning. This paper focuses on the two most recent trends in medical image reconstruction: methods based on sparsity or low-rank models, and data-driven methods based on machine learning techniques.

Overview of Image Reconstruction: From Sparsity to Machine Learning

The paper "Image Reconstruction: From Sparsity to Data-adaptive Methods and Machine Learning" offers an extensive review of the evolution of image reconstruction methodologies, particularly in medical imaging modalities such as MRI, CT, PET, and SPECT. This overview is positioned primarily in the context of advancements towards data-adaptive models and machine learning approaches.

Methodological Categories

The paper identifies four significant categories in the evolution of image reconstruction techniques:

1. Analytical Reconstruction Algorithms: These early methods, such as filtered back-projection (FBP) for CT and inverse Fourier transforms for MRI, are rooted in simple mathematical models. They were computationally efficient but often suboptimal in resolution-noise trade-offs.
2. Iterative Reconstruction Techniques: By integrating models that better account for imaging system physics and sensor statistics, these methods improve image quality by reducing noise and artifacts. Techniques under this vector involve model-based image reconstructions and statistical models, although regulatory approvals predominantly pertain to simpler regularization models.
3. Sparsity and Low-Rank Models: In response to constraints such as reduced sampling in MRI and CT, compressed sensing (CS) and low-rank methods assume sparse representations or low-rank characteristics of images, aiding reconstructions from limited data. These methods have progressed substantially, marking a shift in clinical practices with the FDA approving CS MRI methods.
4. Machine Learning and Data-driven Approaches: The latest paradigms replace traditional mathematical models with adaptive, data-driven models inspired by machine learning. These models, such as deep learning via Convolutional Neural Networks (CNNs), enable capturing complex signal characteristics from extensive datasets, driving improvements in image quality and reconstruction efficiency.

Advances in Machine Learning Integration

The paper navigates through the burgeoning field of machine learning in reconstruction, emphasizing methods like supervised learning, unsupervised learning, and partially supervised hybrid models that integrate physics-driven constraints. These learning-based approaches differentiate themselves by their ability to potentially outperform traditional models, learning representations that are more adaptive and less restrictive.

Computational Implementation

A key focus is the computational feasibility and execution of these complex frameworks. The discussion encapsulates advancements like deep learning architectures and iterative algorithms designed to optimize these non-linear, high-dimensional solutions, reflecting rapid advancements in computational capacities and algorithmic sophistication.

Implications and Future Directions

Theoretical underpinnings are discussed, with a particular emphasis on balance between model sophistication and computational efficiency. The paper acknowledges the necessity for ongoing research in adaptive models and underlines the potential of machine learning to redefine image acquisition strategies and reconstructions in medical imaging. This includes efforts in task-specific optimization, understanding representations, and enhancing model interpretability and adaptation, which are pivotal for clinical adoption.

Conclusion

By thoroughly exploring the transition from legacy image reconstruction techniques to advanced data-driven and machine learning paradigms, the paper provides insights into the theoretical and practical developments shaping the future of medical imaging. While challenges remain, particularly in model adaptability and interpretability, the trends indicate a promising trajectory towards more intelligent and patient-specific imaging solutions facilitated by machine learning. This evolution echoes the broader transdisciplinary collaboration between computational science and biomedical engineering, which will drive further innovation and clinical integration. This field demands continued exploration of these new paradigms to harness their full potential in clinical and non-clinical imaging applications.