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Open problems in Diffusion priors

Balancing initialization and stochasticity in diffusion-based inverse problems1 paper raises it · 1 addresses it
Excessive noise during sampling can erase gains from good initialization, degrading reconstruction quality.
- FLINT: Coupling Proximal Initialization and Bounded Stochasticity for Flow-Matching Inverse Problemsraises · addresses
Joint image-measurement consistency in inverse problems1 paper raises it · 1 addresses it
Most methods condition on noisy measurements but do not enforce consistency between reconstructed image and denoised measurement.
- Dual Flow: Joint Image-Measurement Flow for Inverse Problemsraises · addresses
Handling sparse, asynchronous, or missing sensor data in real-time reconstruction1 paper raises it · 1 addresses it
Real-world sensing systems often have irregular or incomplete measurements, limiting applicability of standard methods.
- Fault-tolerant shallow recurrent decoders for sparse sensing with missing sensor measurementsraises · addresses
Task-driven measurement design for single-pixel imaging1 paper raises it · 1 addresses it
Fixed illumination patterns may not be optimal for classification tasks, wasting acquisition time and photons.
- LIPS-PC: Learning Illumination Patterns for Single-Pixel Classificationraises · addresses
Generalization sensitivity to injected noise in diffusion sampling1 paper raises it · 1 addresses it
Small changes in noise during sampling can break strong generalization across models, affecting reproducibility.
- The role of injected noise in diffusion model generalizationraises · addresses

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computed tomography · ct reconstruction · computed tomography cbct79 papers14 this week
diffusion priors · diffusion prior · imaging inverse77 papers11 this week

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Active contributors · 90 days

Active contributors

Activity · 12 weeks

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arXiv eess.IVOct 2
One Photon, Many Worlds: Posteriors and Predictions with Single-Photon Cameras
Haejoon Lee, Mohit Gupta, Vijayakumar Bhagavatula, Aswin C. Sankaranarayanan
Single-photon avalanche diode (SPAD) cameras operate fundamentally differently from conventional cameras due to their photon-counting nature. Each frame produces a binary image: pixels report zero if no photons arrived during exposure, and one if one or more photons arrived. Reconstructing a scene or inferring its properties from a single binary frame is difficult because many different images could produce the same measurement; thus, the inverse problem is fundamentally one-to-many. As we gather more binary measurements, the inherent uncertainty associated with the inverse problem and any associated inference diminishes. With sufficient photon counts, photon noise becomes negligible relative to the signal mean, enabling near-deterministic scene recovery and inference. This work characterizes the transition from stochastic to near-deterministic scene understanding as photon budget increases, analyzing how the stochasticity in photon arrival affects downstream inference tasks. Technically, we develop a conditional generative framework based on a Hypergeometric frame-thinning process for accumulated binary SPAD measurements. Generative models capture the one-to-many nature of…
PDF arXiv
arXiv math.OCOct 2
A hybrid CNN-adjoint optimization framework for reconstruction of viscoelastic tissue properties in magnetic resonance elastography
Anwesa Dey, Johann Rudi, Elena Cherkaev
Magnetic resonance elastography (MRE) is a noninvasive imaging modality for quantifying the viscoelastic properties of soft tissues from shear wave propagation. Recovering the complex-valued shear modulus from measured displacement fields leads to a severely ill-posed inverse problem, particularly in the presence of noise and limited boundary excitations. We investigate adjoint-based optimization, convolutional neural network (CNN) reconstruction, and a hybrid framework combining both approaches. The forward model is based on a scalar form of the modified stationary Stokes system with a complex shear modulus. We establish well-posedness of the forward problem, existence of minimizers, and first-order optimality conditions for the adjoint-based formulation, and implement a nonlinear conjugate-gradient method with Armijo line search. While PDE-constrained optimization can accurately refine coefficient reconstructions, its performance depends strongly on initialization. We therefore construct a two-dimensional CNN that maps complex-valued displacement measurements to spatially varying complex shear modulus fields and provides rapid, informative initial reconstructions. The proposed…
PDF arXiv
arXiv math.NAOct 1
Flow Matching for Fast Posterior Sampling in Bayesian Inverse Problems
Jan Blechschmidt, Oliver G. Ernst, Moritz Poguntke, Björn Sprungk
Sampling from the posterior is the central task of computational Bayesian inverse problems. The standard workhorse in Bayesian inference - Markov chain Monte Carlo (MCMC) - is sequential, yields correlated samples, and must be rerun for each observation. Conditional flow matching offers an amortized alternative: a transport map, trained once on joint samples of parameter and data, that yields independent approximate posterior samples for any observation at negligible online cost, without new likelihood evaluations. We give a careful, MCMC-literate assessment of flow matching for PDE-based inverse problems with function-valued parameters. Exploiting the flow's tractable density, we derive computable accuracy estimates of the underlying approximate posterior in total-variation distance and Kullback-Leibler divergence and, moreover, propose a hybrid sampler that is asymptotically exact by Metropolization. We validate the accuracy estimates and demonstrate the amortization in several numerical examples, including electrical impedance tomography and a likelihood-free Lotka-Volterra model.
PDF arXiv
arXiv cs.CVOct 1
Moore, Escher, Penrose: A Conformal Golden Braid
Sophia Feldman, Assaf Shocher
I don't think I have ever done anything as peculiar in my life. Among other things, it shows a young man looking with interest at a print on the wall of an exhibition that features himself. How can this be? Perhaps I am not far removed from Einstein's curved universe.'' So wrote M.C. Escher about his 1956 lithograph Print Gallery. Nearly half a century later, a mathematical analysis related its geometry to an untwisted source image through a conformal power map $z \mapsto z^α$, $α\in \mathbb{C}$. Building on this construction, we use a frozen text-to-image diffusion model to generate new self-referential scenes. Prompting alone does not enforce the recursion, while a post-hoc transformation can leave structures poorly connected. Applying the transformation during sampling is also insufficient: the denoiser may "repair" the intended distortion or drift out of the prescribed geometry. We construct a generalized inverse $T^\dagger$ of the non-invertible image transformation $T$, adapted to its recursive constraint. In the idealized formulation, the Penrose identity $TT^\dagger T = T$ makes $TT^\dagger$ an idempotent projection onto geometrically admissible images. Yet denoising only…
PDF arXiv
arXiv cs.CVOct 1
VoxelSynth3D: Interpretable Volumetric Image-Domain Metal Artifact Reduction with a Paired Synthetic CLINIC Benchmark
Amritesh Banerjee, Abdul Basit, Renil Renji Joseph, Nouhaila Innan, Muhammad Shafique
Metal artifacts in postoperative musculoskeletal CT obscure bone-implant and adjacent soft-tissue interfaces. Many metal artifact reduction (MAR) methods require unavailable raw projections or learned models that may shift across scanners and implants. We present VoxelSynth3D, a training-free 3D image-domain framework for reconstructed CT. The framework combines support masking, normalized tissue synthesis, deviation gating, and restricted edge refinement. Detected implant voxels are preserved in the output, while correction targets metal-induced artifacts in the surrounding tissue. We also construct Synthetic CLINIC-Metal, a controlled paired synthetic evaluation resource, from no-metal CTPelvic1K volumes with clean targets, metal/artifact masks, fixed seeds, and patient-level splits; 75 unpaired real metal cases receive qualitative/no-reference evaluation only. The operating point was fixed in a near-flat validation basin. With exact-mask oracle localization, all methods share a metal-excluded tissue ROI. On 40 held-out cases, VoxelSynth3D reduced RMSE from 801.48 to 786.18 HU (paired gain 15.30 HU, 95% CI 11.68-19.23), improving every case and exceeding the evaluated 3D…
PDF arXiv
arXiv math.OCOct 1
Initial condition recovery in nonlinear damped viscous photoacoustic tomography using a convolutional neural network-guided gradient-free optimization framework
Madhu Gupta, Anwesa Dey, Prapti Tala, Souvik Roy
Photoacoustic tomography (PAT) is a hybrid imaging modality that combines high optical contrast with high ultrasonic resolution for biomedical imaging applications. In this work, we investigate the inverse problem of recovering the initial pressure distribution from boundary measurements in the presence of nonlinear acoustic propagation and viscous attenuation effects. To model these phenomena more accurately, we consider a nonlinear damped viscoelastic wave equation incorporating spatially varying sound speed, temporal attenuation, and nonlinear propagation mechanisms. We first establish the well-posedness of the corresponding forward problem using a Galerkin approximation combined with energy estimates and a fixed-point argument. For the inverse problem, we derive existence, uniqueness, and local uniqueness results under suitable assumptions through a harmonic extension reduction, spectral Laplace transform techniques, and observability estimates. To numerically reconstruct the initial pressure field, we develop a hybrid reconstruction framework that combines a convolutional neural network (CNN) with a gradient-free optimization strategy based on the sequential quadratic…
PDF arXiv

Papers

Topics in this field

computed tomography · ct reconstruction · computed tomography cbct79 papers14 this week
diffusion priors · diffusion prior · imaging inverse77 papers11 this week

Active contributors · 90 days

Recent papers

All papers in Research

arXiv eess.IVOct 2
One Photon, Many Worlds: Posteriors and Predictions with Single-Photon Cameras
Haejoon Lee, Mohit Gupta, Vijayakumar Bhagavatula, Aswin C. Sankaranarayanan
Single-photon avalanche diode (SPAD) cameras operate fundamentally differently from conventional cameras due to their photon-counting nature. Each frame produces a binary image: pixels report zero if no photons arrived during exposure, and one if one or more photons arrived. Reconstructing a scene or inferring its properties from a single binary frame is difficult because many different images could produce the same measurement; thus, the inverse problem is fundamentally one-to-many. As we gather more binary measurements, the inherent uncertainty associated with the inverse problem and any associated inference diminishes. With sufficient photon counts, photon noise becomes negligible relative to the signal mean, enabling near-deterministic scene recovery and inference. This work characterizes the transition from stochastic to near-deterministic scene understanding as photon budget increases, analyzing how the stochasticity in photon arrival affects downstream inference tasks. Technically, we develop a conditional generative framework based on a Hypergeometric frame-thinning process for accumulated binary SPAD measurements. Generative models capture the one-to-many nature of…
PDF arXiv
arXiv math.OCOct 2
A hybrid CNN-adjoint optimization framework for reconstruction of viscoelastic tissue properties in magnetic resonance elastography
Anwesa Dey, Johann Rudi, Elena Cherkaev
Magnetic resonance elastography (MRE) is a noninvasive imaging modality for quantifying the viscoelastic properties of soft tissues from shear wave propagation. Recovering the complex-valued shear modulus from measured displacement fields leads to a severely ill-posed inverse problem, particularly in the presence of noise and limited boundary excitations. We investigate adjoint-based optimization, convolutional neural network (CNN) reconstruction, and a hybrid framework combining both approaches. The forward model is based on a scalar form of the modified stationary Stokes system with a complex shear modulus. We establish well-posedness of the forward problem, existence of minimizers, and first-order optimality conditions for the adjoint-based formulation, and implement a nonlinear conjugate-gradient method with Armijo line search. While PDE-constrained optimization can accurately refine coefficient reconstructions, its performance depends strongly on initialization. We therefore construct a two-dimensional CNN that maps complex-valued displacement measurements to spatially varying complex shear modulus fields and provides rapid, informative initial reconstructions. The proposed…
PDF arXiv
arXiv math.NAOct 1
Flow Matching for Fast Posterior Sampling in Bayesian Inverse Problems
Jan Blechschmidt, Oliver G. Ernst, Moritz Poguntke, Björn Sprungk
Sampling from the posterior is the central task of computational Bayesian inverse problems. The standard workhorse in Bayesian inference - Markov chain Monte Carlo (MCMC) - is sequential, yields correlated samples, and must be rerun for each observation. Conditional flow matching offers an amortized alternative: a transport map, trained once on joint samples of parameter and data, that yields independent approximate posterior samples for any observation at negligible online cost, without new likelihood evaluations. We give a careful, MCMC-literate assessment of flow matching for PDE-based inverse problems with function-valued parameters. Exploiting the flow's tractable density, we derive computable accuracy estimates of the underlying approximate posterior in total-variation distance and Kullback-Leibler divergence and, moreover, propose a hybrid sampler that is asymptotically exact by Metropolization. We validate the accuracy estimates and demonstrate the amortization in several numerical examples, including electrical impedance tomography and a likelihood-free Lotka-Volterra model.
PDF arXiv
arXiv cs.CVOct 1
Moore, Escher, Penrose: A Conformal Golden Braid
Sophia Feldman, Assaf Shocher
I don't think I have ever done anything as peculiar in my life. Among other things, it shows a young man looking with interest at a print on the wall of an exhibition that features himself. How can this be? Perhaps I am not far removed from Einstein's curved universe.'' So wrote M.C. Escher about his 1956 lithograph Print Gallery. Nearly half a century later, a mathematical analysis related its geometry to an untwisted source image through a conformal power map $z \mapsto z^α$, $α\in \mathbb{C}$. Building on this construction, we use a frozen text-to-image diffusion model to generate new self-referential scenes. Prompting alone does not enforce the recursion, while a post-hoc transformation can leave structures poorly connected. Applying the transformation during sampling is also insufficient: the denoiser may "repair" the intended distortion or drift out of the prescribed geometry. We construct a generalized inverse $T^\dagger$ of the non-invertible image transformation $T$, adapted to its recursive constraint. In the idealized formulation, the Penrose identity $TT^\dagger T = T$ makes $TT^\dagger$ an idempotent projection onto geometrically admissible images. Yet denoising only…
PDF arXiv
arXiv cs.CVOct 1
VoxelSynth3D: Interpretable Volumetric Image-Domain Metal Artifact Reduction with a Paired Synthetic CLINIC Benchmark
Amritesh Banerjee, Abdul Basit, Renil Renji Joseph, Nouhaila Innan, Muhammad Shafique
Metal artifacts in postoperative musculoskeletal CT obscure bone-implant and adjacent soft-tissue interfaces. Many metal artifact reduction (MAR) methods require unavailable raw projections or learned models that may shift across scanners and implants. We present VoxelSynth3D, a training-free 3D image-domain framework for reconstructed CT. The framework combines support masking, normalized tissue synthesis, deviation gating, and restricted edge refinement. Detected implant voxels are preserved in the output, while correction targets metal-induced artifacts in the surrounding tissue. We also construct Synthetic CLINIC-Metal, a controlled paired synthetic evaluation resource, from no-metal CTPelvic1K volumes with clean targets, metal/artifact masks, fixed seeds, and patient-level splits; 75 unpaired real metal cases receive qualitative/no-reference evaluation only. The operating point was fixed in a near-flat validation basin. With exact-mask oracle localization, all methods share a metal-excluded tissue ROI. On 40 held-out cases, VoxelSynth3D reduced RMSE from 801.48 to 786.18 HU (paired gain 15.30 HU, 95% CI 11.68-19.23), improving every case and exceeding the evaluated 3D…
PDF arXiv
arXiv math.OCOct 1
Initial condition recovery in nonlinear damped viscous photoacoustic tomography using a convolutional neural network-guided gradient-free optimization framework
Madhu Gupta, Anwesa Dey, Prapti Tala, Souvik Roy
Photoacoustic tomography (PAT) is a hybrid imaging modality that combines high optical contrast with high ultrasonic resolution for biomedical imaging applications. In this work, we investigate the inverse problem of recovering the initial pressure distribution from boundary measurements in the presence of nonlinear acoustic propagation and viscous attenuation effects. To model these phenomena more accurately, we consider a nonlinear damped viscoelastic wave equation incorporating spatially varying sound speed, temporal attenuation, and nonlinear propagation mechanisms. We first establish the well-posedness of the corresponding forward problem using a Galerkin approximation combined with energy estimates and a fixed-point argument. For the inverse problem, we derive existence, uniqueness, and local uniqueness results under suitable assumptions through a harmonic extension reduction, spectral Laplace transform techniques, and observability estimates. To numerically reconstruct the initial pressure field, we develop a hybrid reconstruction framework that combines a convolutional neural network (CNN) with a gradient-free optimization strategy based on the sequential quadratic…
PDF arXiv

Activity · 12 weeks

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Diffusion priors

Found by the topic model: diffusion priors, computed tomography.

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Open problems in Diffusion priors

Balancing initialization and stochasticity in diffusion-based inverse problems1 paper raises it · 1 addresses it
Excessive noise during sampling can erase gains from good initialization, degrading reconstruction quality.
- FLINT: Coupling Proximal Initialization and Bounded Stochasticity for Flow-Matching Inverse Problemsraises · addresses
Joint image-measurement consistency in inverse problems1 paper raises it · 1 addresses it
Most methods condition on noisy measurements but do not enforce consistency between reconstructed image and denoised measurement.
- Dual Flow: Joint Image-Measurement Flow for Inverse Problemsraises · addresses
Handling sparse, asynchronous, or missing sensor data in real-time reconstruction1 paper raises it · 1 addresses it
Real-world sensing systems often have irregular or incomplete measurements, limiting applicability of standard methods.
- Fault-tolerant shallow recurrent decoders for sparse sensing with missing sensor measurementsraises · addresses
Task-driven measurement design for single-pixel imaging1 paper raises it · 1 addresses it
Fixed illumination patterns may not be optimal for classification tasks, wasting acquisition time and photons.
- LIPS-PC: Learning Illumination Patterns for Single-Pixel Classificationraises · addresses
Generalization sensitivity to injected noise in diffusion sampling1 paper raises it · 1 addresses it
Small changes in noise during sampling can break strong generalization across models, affecting reproducibility.
- The role of injected noise in diffusion model generalizationraises · addresses

Named by an AI from these papers' abstracts.