Optimal compressed sensing for image reconstruction with diffusion probabilistic models

• URL: http://arxiv.org/abs/2405.17456v2
• Date: Sat, 01 Feb 2025 00:37:30 GMT
• Title: Optimal compressed sensing for image reconstruction with diffusion probabilistic models
• Authors: Ling-Qi Zhang, Zahra Kadkhodaie, Eero P. Simoncelli, David H. Brainard,
• Abstract summary: Well-established methods for optimizing such measurements include principal component analysis (PCA), independent component analysis (ICA) and compressed sensing (CS) We introduce a general method for obtaining an optimized set of linear measurements for efficient image reconstruction. We demonstrate that the optimal measurements derived for two natural image datasets differ from those of PCA, ICA, or CS, and result in substantially lower mean squared reconstruction error.
• Score: 10.297832938258841
• License:
• Abstract: We examine the problem of selecting a small set of linear measurements for reconstructing high-dimensional signals. Well-established methods for optimizing such measurements include principal component analysis (PCA), independent component analysis (ICA) and compressed sensing (CS) based on random projections, all of which rely on axis- or subspace-aligned statistical characterization of the signal source. However, many naturally occurring signals, including photographic images, contain richer statistical structure. To exploit such structure, we introduce a general method for obtaining an optimized set of linear measurements for efficient image reconstruction, where the signal statistics are expressed by the prior implicit in a neural network trained to perform denoising (generally known as a "diffusion model"). We demonstrate that the optimal measurements derived for two natural image datasets differ from those of PCA, ICA, or CS, and result in substantially lower mean squared reconstruction error. Interestingly, the marginal distributions of the measurement values are asymmetrical (skewed), substantially more so than those of previous methods. We also find that optimizing with respect to perceptual loss, as quantified by structural similarity (SSIM), leads to measurements different from those obtained when optimizing for MSE. Our results highlight the importance of incorporating the specific statistical regularities of natural signals when designing effective linear measurements.

Related papers

• Advancing quantum imaging through learning theory [7.19995826332098]
  We quantify performance of quantum imaging by modeling it as a learning task and calculating the Resolvable Expressive Capacity (REC) We first examine imaging performance for two-point sources and generally distributed sources, referred to as compact sources.
  arXiv  Detail & Related papers  (2025-01-26T22:02:13Z)
• Spectral Estimators for Structured Generalized Linear Models via Approximate Message Passing [28.91482208876914]
  We consider the problem of parameter estimation in a high-dimensional generalized linear model. Despite their wide use, a rigorous performance characterization, as well as a principled way to preprocess the data, are available only for unstructured designs.
  arXiv  Detail & Related papers  (2023-08-28T11:49:23Z)
• ESSAformer: Efficient Transformer for Hyperspectral Image Super-resolution [76.7408734079706]
  Single hyperspectral image super-resolution (single-HSI-SR) aims to restore a high-resolution hyperspectral image from a low-resolution observation. We propose ESSAformer, an ESSA attention-embedded Transformer network for single-HSI-SR with an iterative refining structure.
  arXiv  Detail & Related papers  (2023-07-26T07:45:14Z)
• MOSAIC: Masked Optimisation with Selective Attention for Image Reconstruction [0.5541644538483947]
  We propose a novel compressive sensing framework to reconstruct images given any random selection of measurements. MOSAIC incorporates an embedding technique to efficiently apply attention mechanisms on an encoded sequence of measurements. A range of experiments validate our proposed architecture as a promising alternative for existing CS reconstruction methods.
  arXiv  Detail & Related papers  (2023-06-01T17:05:02Z)
• DeepDC: Deep Distance Correlation as a Perceptual Image Quality Evaluator [53.57431705309919]
  ImageNet pre-trained deep neural networks (DNNs) show notable transferability for building effective image quality assessment (IQA) models. We develop a novel full-reference IQA (FR-IQA) model based exclusively on pre-trained DNN features. We conduct comprehensive experiments to demonstrate the superiority of the proposed quality model on five standard IQA datasets.
  arXiv  Detail & Related papers  (2022-11-09T14:57:27Z)
• Effective Invertible Arbitrary Image Rescaling [77.46732646918936]
  Invertible Neural Networks (INN) are able to increase upscaling accuracy significantly by optimizing the downscaling and upscaling cycle jointly. A simple and effective invertible arbitrary rescaling network (IARN) is proposed to achieve arbitrary image rescaling by training only one model in this work. It is shown to achieve a state-of-the-art (SOTA) performance in bidirectional arbitrary rescaling without compromising perceptual quality in LR outputs.
  arXiv  Detail & Related papers  (2022-09-26T22:22:30Z)
• A Model for Multi-View Residual Covariances based on Perspective Deformation [88.21738020902411]
  We derive a model for the covariance of the visual residuals in multi-view SfM, odometry and SLAM setups. We validate our model with synthetic and real data and integrate it into photometric and feature-based Bundle Adjustment.
  arXiv  Detail & Related papers  (2022-02-01T21:21:56Z)
• Fast Scalable Image Restoration using Total Variation Priors and Expectation Propagation [7.7731951589289565]
  This paper presents a scalable approximate Bayesian method for image restoration using total variation (TV) priors. We use the expectation propagation (EP) framework to approximate minimum mean squared error (MMSE) estimators and marginal (pixel-wise) variances.
  arXiv  Detail & Related papers  (2021-10-04T17:28:41Z)
• Understanding Implicit Regularization in Over-Parameterized Single Index Model [55.41685740015095]
  We design regularization-free algorithms for the high-dimensional single index model. We provide theoretical guarantees for the induced implicit regularization phenomenon.
  arXiv  Detail & Related papers  (2020-07-16T13:27:47Z)
• Asymptotic Analysis of an Ensemble of Randomly Projected Linear Discriminants [94.46276668068327]
  In [1], an ensemble of randomly projected linear discriminants is used to classify datasets. We develop a consistent estimator of the misclassification probability as an alternative to the computationally-costly cross-validation estimator. We also demonstrate the use of our estimator for tuning the projection dimension on both real and synthetic data.
  arXiv  Detail & Related papers  (2020-04-17T12:47:04Z)
• Bayesian System ID: Optimal management of parameter, model, and measurement uncertainty [0.0]
  We evaluate the robustness of a probabilistic formulation of system identification (ID) to sparse, noisy, and indirect data. We show that the log posterior has improved geometric properties compared with the objective function surfaces of traditional methods.
  arXiv  Detail & Related papers  (2020-03-04T22:48:30Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.