DICE: Diffusion Consensus Equilibrium for Sparse-view CT Reconstruction

Sparse-view computed tomography (CT) reconstruction is fundamentally challenging due to undersampling, leading to an ill-posed inverse problem. Traditional iterative methods incorporate handcrafted or learned priors to regularize the solution but struggle to capture the complex structures present in medical images. In contrast, diffusion models (DMs) have recently emerged as powerful generative priors that can accurately model complex image distributions. In this work, we introduce Diffusion Consensus Equilibrium (DICE), a framework that integrates a two-agent consensus equilibrium into the sampling process of a DM. DICE alternates between: (i) a data-consistency agent, implemented through a proximal operator enforcing measurement consistency, and (ii) a prior agent, realized by a DM performing a clean image estimation at each sampling step. By balancing these two complementary agents iteratively, DICE effectively combines strong generative prior capabilities with measurement consistency. Experimental results show that DICE significantly outperforms state-of-the-art baselines in reconstructing high-quality CT images under uniform and non-uniform sparse-view settings of 15, 30, and 60 views (out of a total of 180), demonstrating both its effectiveness and robustness.

UTOPY: Unrolling Algorithm Learning via Fidelity Homotopy for Inverse Problems

Imaging Inverse problems aim to reconstruct an underlying image from undersampled, coded, and noisy observations. Within the wide range of reconstruction frameworks, the unrolling algorithm is one of the most popular due to the synergistic integration of traditional model-based reconstruction methods and modern neural networks, providing an interpretable and highly accurate reconstruction. However, when the sensing operator is highly ill-posed, gradient steps on the data-fidelity term can hinder convergence and degrade reconstruction quality. To address this issue, we propose UTOPY, a homotopy continuation formulation for training the unrolling algorithm. Mainly, this method involves using a well-posed (synthetic) sensing matrix at the beginning of the unrolling network optimization. We define a continuation path strategy to transition smoothly from the synthetic fidelity to the desired ill-posed problem. This strategy enables the network to progressively transition from a simpler, well-posed inverse problem to the more challenging target scenario. We theoretically show that, for projected gradient descent-like unrolling models, the proposed continuation strategy generates a smooth path of unrolling solutions. Experiments on compressive sensing and image deblurring demonstrate that our method consistently surpasses conventional unrolled training, achieving up to 2.5 dB PSNR improvement in reconstruction performance. Source code at

Single Snapshot Distillation for Phase Coded Mask Design in Phase Retrieval

Phase retrieval (PR) reconstructs phase information from magnitude measurements, known as coded diffraction patterns (CDPs), whose quality depends on the number of snapshots captured using coded phase masks. High-quality phase estimation requires multiple snapshots, which is not desired for efficient PR systems. End-to-end frameworks enable joint optimization of the optical system and the recovery neural network. However, their application is constrained by physical implementation limitations. Additionally, the framework is prone to gradient vanishing issues related to its global optimization process. This paper introduces a Knowledge Distillation (KD) optimization approach to address these limitations. KD transfers knowledge from a larger, lower-constrained network (teacher) to a smaller, more efficient, and implementable network (student). In this method, the teacher, a PR system trained with multiple snapshots, distills its knowledge into a single-snapshot PR system, the student. The loss functions compare the CPMs and the feature space of the recovery network. Simulations demonstrate that this approach improves reconstruction performance compared to a PR system trained without the teacher's guidance.

Distilling Knowledge for Designing Computational Imaging Systems

Designing the physical encoder is crucial for accurate image reconstruction in computational imaging (CI) systems. Currently, these systems are designed via end-to-end (E2E) optimization, where the encoder is modeled as a neural network layer and is jointly optimized with the decoder. However, the performance of E2E optimization is significantly reduced by the physical constraints imposed on the encoder. Also, since the E2E learns the parameters of the encoder by backpropagating the reconstruction error, it does not promote optimal intermediate outputs and suffers from gradient vanishing. To address these limitations, we reinterpret the concept of knowledge distillation (KD) for designing a physically constrained CI system by transferring the knowledge of a pretrained, less-constrained CI system. Our approach involves three steps: (1) Given the original CI system (student), a teacher system is created by relaxing the constraints on the student's encoder. (2) The teacher is optimized to solve a less-constrained version of the student's problem. (3) The teacher guides the training of the student through two proposed knowledge transfer functions, targeting both the encoder and the decoder feature space. The proposed method can be employed to any imaging modality since the relaxation scheme and the loss functions can be adapted according to the physical acquisition and the employed decoder. This approach was validated on three representative CI modalities: magnetic resonance, single-pixel, and compressive spectral imaging. Simulations show that a teacher system with an encoder that has a structure similar to that of the student encoder provides effective guidance. Our approach achieves significantly improved reconstruction performance and encoder design, outperforming both E2E optimization and traditional non-data-driven encoder designs.

Highly Constrained Coded Aperture Imaging Systems Design Via a Knowledge Distillation Approach

Computational optical imaging (COI) systems have enabled the acquisition of high-dimensional signals through optical coding elements (OCEs). OCEs encode the high-dimensional signal in one or more snapshots, which are subsequently decoded using computational algorithms. Currently, COI systems are optimized through an end-to-end (E2E) approach, where the OCEs are modeled as a layer of a neural network and the remaining layers perform a specific imaging task. However, the performance of COI systems optimized through E2E is limited by the physical constraints imposed by these systems. This paper proposes a knowledge distillation (KD) framework for the design of highly physically constrained COI systems. This approach employs the KD methodology, which consists of a teacher-student relationship, where a high-performance, unconstrained COI system (the teacher), guides the optimization of a physically constrained system (the student) characterized by a limited number of snapshots. We validate the proposed approach, using a binary coded apertures single pixel camera for monochromatic and multispectral image reconstruction. Simulation results demonstrate the superiority of the KD scheme over traditional E2E optimization for the designing of highly physically constrained COI systems.

GAN-supervised Seismic Data Reconstruction: An Enhanced-Learning for Improved Generalization

Seismic data interpolation plays a crucial role in subsurface imaging, enabling accurate analysis and interpretation throughout the seismic processing workflow. Despite the widespread exploration of deep supervised learning methods for seismic data reconstruction, several challenges still remain open. Particularly, the requirement of extensive training data and poor domain generalization due to the seismic survey's variability poses significant issues. To overcome these limitations, this paper introduces a deep-learning-based seismic data reconstruction approach that leverages data redundancy. This method involves a two-stage training process. First, an adversarial generative network (GAN) is trained using synthetic seismic data, enabling the extraction and learning of their primary and local seismic characteristics. Second, a reconstruction network is trained with synthetic data generated by the GAN, which dynamically adjusts the noise and distortion level at each epoch to promote feature diversity. This approach enhances the generalization capabilities of the reconstruction network by allowing control over the generation of seismic patterns from the latent space of the GAN, thereby reducing the dependency on large seismic databases. Experimental results on field and synthetic seismic datasets both pre-stack and post-stack show that the proposed method outperforms the baseline supervised learning and unsupervised approaches such as deep seismic prior and internal learning, by up to 8 dB of PSNR.