Deep learning has proven to be an efficient and robust method for many computational imaging systems. The advantages of machine learning, as a rule, are that it is fast—at least in its supervised form after training is complete—and seems exceedingly effective in capturing regularizing priors. Here, we focus the discussion on non-invasive three-dimensional (3D) object reconstruction. One then faces the additional dilemma of choosing the appropriate model of light-matter interaction inside the specimen, i.e. the forward operator. We describe the three stages of approximation that are applicable: weak scattering with weak diffraction (also known as the Radon transform), weak scattering with strong diffraction, and strong scattering. We then overview machine learning approaches for the various models, and glance at the consequences of oversimplifying the forward operator choice.
Structured illumination (SI) phase imaging is an important strategy to achieve quantitative phase imaging via encoding phase-induced diffraction into modulation intensity signals through propagation. However, the nonlinear property of SI-based transfer function results in ill-posedness in phase imaging retrieval. Overlapping modulation spectrum usually leads to loss of high spatial frequency components. Recent studies show that such nonlinear inversion problems can be efficiently represented by deep neural networks, as have been demonstrated in phase retrieval via holography and Fourier ptychography techniques. Here we present a hierarchical synthesis network (HSNet) which uses multiple splitting networks to extract structural features of structured intensity images in various modulation frequency and synthesis network to produce high fidelity reconstruction. We show that the proposed framework retrieve clear and accurate phase profile with reduced computing requirements in simulation.
Quantitative phase imaging (QPI) provides enhanced contrast for weakly absorbing specimens such as biological tissues under optical light and soft materials under X-ray. In this work, we develop a model-based phase retrieval framework by integrating the physics principles of phase imaging with the deep learning-based approach. Both measurements and the forward model are used as the inputs for a model-based neural network. The features of the object and the regularization weight of the established priors are learned by minimizing the difference between the network output to the ground truth during the training process. This method is tested on phase imaging of handwriting digital patterns and biological cells in a simulation of propagation-based TIE (transport of intensity equation) phase retrieval. We achieve enhanced accuracy for the phase retrieval compared to non-model based end-to-end neural networks and reduce the computation cost compared to traditional model-based iterative reconstruction algorithms.
Porous structures are widely found in natural and engineered material systems. To study the defect initialization and damage evolution in the complex 3D network structures, we explore advanced X-ray phase tomography to provide holistic and high-resolution 3D data. A pipeline of deep learning-based phase retrieval, computer vision, and damage identification algorithms are implemented to extract various types of damage for large volumetric tomography data. We first obtain high-quality phase tomography reconstruction from noisy and insufficient CT acquisition. Based on a hybrid approach using both model-based feature filtering and data-driven machine learning, we then identifies the defects and damaged regions from the background of porous structures. This method is applied to an in-situ X-ray tomography measurement on a natural cellular material; the accurate and comprehensive defects detection reveals insight into 3D damage evolution modes for porous material systems.
Structured-illumination (SI) is used for quantitative phase retrieval for improved contrast and sensitivity. However, the nonlinear nature of SI-based phase retrieval process, such as the spatial frequency biases and mixture of different spatial frequency components, usually leads to phase aberrations, in particular in the high spatial frequency components. Recent studies show that nonlinear inversion problems can be efficiently represented by deep neural networks in an end-to-end framework. In this study, we present a deep learning framework for SI-based quantitative phase imaging via the Conditional Generative Adversarial Network (cGANs). A series of structured images paired with the corresponding ground truth of phase images are used to train two competing networks of generator and discriminator. We demonstrate that the GAN-based approach produces sharp and accurate phase image and the structured illumination pattern simultaneously based on our simulation.
X-ray computed tomography has been recently applied to capture the dynamic behaviors of complex material systems in 4D. The dynamic 3D acquisition, however, usually leads to insufficient data acquisition with low-dose X-ray radiation and limited-angle projections. A high-fidelity CT reconstruction is challenging based on the severely limited acquisition. While prior constraint, such as local smoothness, can improve the quality of reconstructions, a more general reconstruction strategy to include structural features on a range of different scales proves to yield better reconstruction results and are more adaptive to complex structured materials. In this work, we develop the hierarchical synthesis network to establish structural priors for sparse-view CT reconstruction, which achieves high-fidelity with an improved computation efficiency. We found that the established knowledge of structural priors on each different scale can be independently transferred to sparse-view CT reconstruction under different conditions, enabling the transfer of non-local features into the reconstruction of a phase tomography application.
We present a hierarchical imaging reconstruction algorithm for a 3D phase tomography based on the densely extracted features on a multi-band pyramid of convolutional network. By implementing a layer-wise hierarchical machine learning network and combine different bands of information for the imaging retrieval, a more efficient and adaptive learning strategy is established to enable an accurate reconstruction with fewer training data and improved accuracy. In addition, the distinction of intensity and spectral bands in the feature training process enables bias correction for reconstruction under varied conditions. In particular, we demonstrate a robust imaging reconstruction for a sparse-view phase tomography application, where spectrally biased phase diffraction and intensity-biased photon noise are both successfully corrected for.
We present a high-temporal resolution 4D-XCT with feature-based iterative reconstruction method(FBIR) by imposing feature priors in the reconstruction process. The 4D reconstruction is acquired through an iterative minimization of the cost function which is obtained by combining the forward model and multiple structural featurebased priors. The scheme is applied to the study of the mechanical response of a porous structure (sea urchin spines), which achieves high temporal resolution and demonstrates robustness against noise, limited views and motion induced blurring.
A one-shot multi-directional ultra-small angle X-ray scattering imaging successfully resolves the fiber orientation of a wood sample. This 2D structured illumination enables the retrieval of scattering signals in multiple directions simultaneously.
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