arXiv:2509. 15026v2 Announce Type: replace-cross Abstract: We seek to recover an unknown signal from nonlinear amplitude-only measurements, a challenging inverse problem.
arXiv:2606. 07257v1 Announce Type: cross Abstract: Phase retrieval - recovering a complex-valued field from intensity measurements - is typically solved using variants of the Gerchberg-Saxton (GS) algorithm, understood as alternating projections between measurement planes.
arXiv:2510. 02208v3 Announce Type: replace-cross Abstract: Diffusion models have emerged as powerful generative priors for solving inverse imaging problems.
MG-SpaIR is a training-data-free framework for restoring a clean image from a single observation corrupted by a mixture of blur, downsampling, noise, and missing pixels. Building on implicit neural representations (INRs), we introduce a multi-grade coarse-to-fine residual hierarchy that progressively refines the reconstruction across resolution grades, improving representational fidelity and mitigating spectral limitations.
The paper introduces tunable latent priors for diffusion models, normalizing flows, and variational autoencoders using nested dropout. These priors allow the latent dimensionality to adapt to each inverse problem, reducing reconstruction errors compared to fixed-complexity models across tasks such as compressed sensing, inpainting, denoising, and phase retrieval. In linear denoising, the authors derive the optimal latent complexity in closed form, linking it to noise level and signal spectrum.
The paper investigates compressed sensing using a family of tunable linear generative priors linked through their singular value decompositions. It proves that in noiseless Gaussian compressed sensing, the full-dimensional linear prior yields the lowest expected reconstruction error across the entire family, meaning lower-complexity priors do not improve performance in this idealized setting. This contrasts with denoising, where lower complexity priors can reduce error due to bias‑variance tradeoffs, suggesting that the experimental gains seen with neural network priors stem from their nonlinearities.
arXiv:2607. 19333v1 Announce Type: cross Abstract: Diffusion-based methods have achieved remarkable empirical success in solving inverse problems.
The paper introduces the Ensemble-conditioned Inverse Problem (EIP), a multivariate statistical framework for inferring an ensemble that follows the pushforward of a prior through a forward process. It applies to fields such as high‑energy physics, full waveform inversion, and inverse imaging, and proposes non‑iterative inference‑time methods using ensemble inverse generative models that avoid explicit forward model use during inference. The authors demonstrate the approach on synthetic and real datasets and provide code for replication.
arXiv:2607. 26887v1 Announce Type: cross Abstract: Many high-resolution imaging systems face the same fundamental question: when have enough measurements been collected to reconstruct an image accurately?
arXiv:2312. 15341v1 Announce Type: cross Abstract: We provide an overview of recent progress in statistical inverse problems with random experimental design, covering both linear and nonlinear inverse problems.
The paper introduces a learning-based approach to replace the MCMC step in split-Gibbs diffusion posterior sampling. By reformulating both Gibbs updates as Gaussian denoising problems, the method uses ODE diffusion for the prior step with a pretrained denoiser and a lightweight deep-unfolded network for the likelihood step. Experiments on nonlinear phase retrieval show that this alternative reduces likelihood-update cost while maintaining effectiveness compared to MCMC-based split Gibbs.
arXiv:2508. 05321v4 Announce Type: replace-cross Abstract: Assume you encounter an inverse problem that shall be solved for a large number of data, but no ground-truth data is available.
The paper introduces a self‑supervised approach for Poisson inverse imaging problems that leverages frozen CLIP RN50 features as a lightweight prior within an ADMM‑inspired unrolled solver. By decoupling data‑consistency from the prior and using a parameter‑efficient decoder, the method adapts foundation vision representations without extensive fine‑tuning. Experiments on Poisson CFA demosaicing and deblurring demonstrate competitive image quality, enhanced robustness to dataset and acquisition shifts, and self‑supervised performance close to that of supervised training.