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1. Dynamic low-count PET image reconstruction using spatio-temporal primal dual network

   Hu R.; Cui J.; Li C.; Yu C.; Chen Y.; Liu H. (October 2023, Physics in medicine and biology)

   Objective. Dynamic positron emission tomography (PET) imaging, which can provide information on dynamic changes in physiological metabolism, is now widely used in clinical diagnosis and cancer treatment. However, the reconstruction from dynamic data is extremely challenging due to the limited counts received in individual frame, especially in ultra short frames. Recently, the unrolled modelbased deep learning methods have shown inspiring results for low-count PET image reconstruction with good interpretability. Nevertheless, the existing model-based deep learning methods mainly focus on the spatial correlations while ignore the temporal domain. Approach. In this paper, inspired by the learned primal dual (LPD) algorithm, we propose the spatio-temporal primal dual network (STPDnet) for dynamic low-count PET image reconstruction. Both spatial and temporal correlations are encoded by 3D convolution operators. The physical projection of PET is embedded in the iterative learning process of the network, which provides the physical constraints and enhances interpretability. Main results. The experiments of both simulation data and real rat scan data have shown that the proposed method can achieve substantial noise reduction in both temporal and spatial domains and outperform the maximum likelihood expectation maximization, spatio-temporal kernel method, LPD and FBPnet. Significance. Experimental results show STPDnet better reconstruction performance in the low count situation, which makes the proposed method particularly suitable in whole-body dynamic imaging and parametric PET imaging that require extreme short frames and usually suffer from high level of noise. 

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2. Blind Primed Supervised (BLIPS) Learning for MR Image Reconstrution

   Lahiri, Anish; Wang, Guanhua; Ravishankar, Saiprasad; Fessler, Jeffrey (January 2021, International Society for Magnetic Resonance in Medicine)

   The work examines a combined supervised-unsupervised framework involving dictionary-based blind learning and deep supervised learning or MR image reconstruction from under-sampled k-space data. A major focus of the work is to investigate the possible synergy of learned features in traditional shallow reconstruction using sparsity-based priors and deep prior-based reconstruction. Specifically, we propose a framework that uses an unrolled network to refine a blind dictionary learning based reconstruction. we compare the proposed method with strictly supervised deep learning-based reconstruction approaches on several datasets of varying sized and anatomies. 

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3. Image Reconstruction Via Autoencoding Sequential Deep Image Prior

   Alkhouri, Ismail; Liang, Shijun; Bell, Evan; Qu, Qing; Wang, Rongrong; Ravishankar, Saiprasad (December 2024, Advances in Neural Information Processing Systems)

   Recently, Deep Image Prior (DIP) has emerged as an effective unsupervised one-shot learner, delivering competitive results across various image recovery problems. This method only requires the noisy measurements and a forward operator, relying solely on deep networks initialized with random noise to learn and restore the structure of the data. However, DIP is notorious for its vulnerability to overfitting due to the overparameterization of the network. Building upon insights into the impact of the DIP input and drawing inspiration from the gradual denoising process in cutting-edge diffusion models, we introduce Autoencoding Sequential DIP (aSeqDIP) for image reconstruction. This method progressively denoises and reconstructs the image through a sequential optimization of network weights. This is achieved using an input-adaptive DIP objective, combined with an autoencoding regularization term. Compared to diffusion models, our method does not require training data and outperforms other DIP-based methods in mitigating noise overfitting while maintaining a similar number of parameter updates as Vanilla DIP. Through extensive experiments, we validate the effectiveness of our method in various image reconstruction tasks, such as MRI and CT reconstruction, as well as in image restoration tasks like image denoising, inpainting, and non-linear deblurring. 

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4. Random mesh projectors for inverse problems

   Konik Kothari, Sidharth Gupta (May 2019, 7th International Conference on Learning Representations, ICLR 2019)

   We propose a new learning-based approach to solve ill-posed inverse problems in imaging. We address the case where ground truth training samples are rare and the problem is severely ill-posed-both because of the underlying physics and because we can only get few measurements. This setting is common in geophysical imaging and remote sensing. We show that in this case the common approach to directly learn the mapping from the measured data to the reconstruction becomes unstable. Instead, we propose to first learn an ensemble of simpler mappings from the data to projections of the unknown image into random piecewise-constant subspaces. We then combine the projections to form a final reconstruction by solving a deconvolution-like problem. We show experimentally that the proposed method is more robust to measurement noise and corruptions not seen during training than a directly learned inverse. 

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5. Physics informed image restoration under low illumination with simultaneous parameter estimation using 3D integral imaging and Bayesian neural networks

   https://doi.org/10.1364/OE.546780  

   Krishnan, Gokul; Lee, Jiheon; Goswami, Saurabh; Javidi, Bahram (February 2025, Optics Express)

   Image restoration aims to recover a clean image given a noisy image. It has long been a topic of interest for researchers in imaging, optical science and computer vision. As the imaging environment becomes more and more deteriorated, the problem becomes more challenging. Several computational approaches, ranging from statistical to deep learning, have been proposed over the years to tackle this problem. The deep learning-based approaches provided promising image restoration results, but it’s purely data driven and the requirement of large datasets (paired or unpaired) for training might demean its utility for certain physical problems. Recently, physics informed image restoration techniques have gained importance due to their ability to enhance performance, infer some sense of the degradation process and its potential to quantify the uncertainty in the prediction results. In this paper, we propose a physics informed deep learning approach with simultaneous parameter estimation using 3D integral imaging and Bayesian neural network (BNN). An image-image mapping architecture is first pretrained to generate a clean image from the degraded image, which is then utilized for simultaneous training with Bayesian neural network for simultaneous parameter estimation. For the network training, simulated data using the physical model has been utilized instead of actual degraded data. The proposed approach has been tested experimentally under degradations such as low illumination and partial occlusion. The recovery results are promising despite training from a simulated dataset. We have tested the performance of the approach under varying levels of illumination condition. Additionally, the proposed approach also has been analyzed against corresponding 2D imaging-based approach. The results suggest significant improvements compared to 2D even training under similar datasets. Also, the parameter estimation results demonstrate the utility of the approach in estimating the degradation parameter in addition to image restoration under the experimental conditions considered. 

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