Exploring Invariance in Images through One-way Wave Equations

• URL: http://arxiv.org/abs/2310.12976v2
• Date: Tue, 15 Oct 2024 22:26:58 GMT
• Title: Exploring Invariance in Images through One-way Wave Equations
• Authors: Yinpeng Chen, Dongdong Chen, Xiyang Dai, Mengchen Liu, Yinan Feng, Youzuo Lin, Lu Yuan, Zicheng Liu,
• Abstract summary: In this paper, we empirically reveal an invariance over images-images share a set of one-way wave equations with latent speeds. We demonstrate it using an intuitive encoder-decoder framework where each image is encoded into its corresponding initial condition.
• Score: 96.90549064390608
• License:
• Abstract: In this paper, we empirically reveal an invariance over images-images share a set of one-way wave equations with latent speeds. Each image is uniquely associated with a solution to these wave equations, allowing for its reconstruction with high fidelity from an initial condition. We demonstrate it using an intuitive encoder-decoder framework where each image is encoded into its corresponding initial condition (a single vector). Subsequently, the initial condition undergoes a specialized decoder, transforming the one-way wave equations into a first-order norm + linear autoregressive process. This process propagates the initial condition along the x and y directions, generating a high-resolution feature map (up to the image resolution), followed by a few convolutional layers to reconstruct image pixels. The revealed invariance, rooted in the shared wave equations, offers a fresh perspective for comprehending images, establishing a promising avenue for further exploration.

Related papers

• Wavelets Are All You Need for Autoregressive Image Generation [1.187456026346823]
  We take a new approach to autoregressive image generation that is based on two main ingredients. The first is wavelet image coding, which allows to tokenize the visual details of an image from coarse to fine details. The second is a variant of a language transformer whose architecture is re-designed and optimized for token sequences.
  arXiv  Detail & Related papers  (2024-06-28T15:32:59Z)
• Deep Equilibrium Diffusion Restoration with Parallel Sampling [120.15039525209106]
  Diffusion model-based image restoration (IR) aims to use diffusion models to recover high-quality (HQ) images from degraded images, achieving promising performance. Most existing methods need long serial sampling chains to restore HQ images step-by-step, resulting in expensive sampling time and high computation costs. In this work, we aim to rethink the diffusion model-based IR models through a different perspective, i.e., a deep equilibrium (DEQ) fixed point system, called DeqIR.
  arXiv  Detail & Related papers  (2023-11-20T08:27:56Z)
• Improving Denoising Diffusion Models via Simultaneous Estimation of Image and Noise [15.702941058218196]
  This paper introduces two key contributions aimed at improving the speed and quality of images generated through inverse diffusion processes. The first contribution involves re parameterizing the diffusion process in terms of the angle on a quarter-circular arc between the image and noise. The second contribution is to directly estimate both the image ($mathbfx_0$) and noise ($mathbfepsilon$) using our network.
  arXiv  Detail & Related papers  (2023-10-26T05:43:07Z)
• Reflected Diffusion Models [93.26107023470979]
  We present Reflected Diffusion Models, which reverse a reflected differential equation evolving on the support of the data. Our approach learns the score function through a generalized score matching loss and extends key components of standard diffusion models.
  arXiv  Detail & Related papers  (2023-04-10T17:54:38Z)
• Alternating Phase Langevin Sampling with Implicit Denoiser Priors for Phase Retrieval [1.7767466724342065]
  We present a way leveraging the prior implicitly learned by a denoiser to solve phase retrieval problems by incorporating it in a classical framework. Compared to performant denoising-based algorithms for phase retrieval, we showcase competitive performance with notable measurements on in-distribution images and notable out-of-distribution images.
  arXiv  Detail & Related papers  (2022-11-02T05:08:50Z)
• Regularization via deep generative models: an analysis point of view [8.818465117061205]
  This paper proposes a new way of regularizing an inverse problem in imaging (e.g., deblurring or inpainting) by means of a deep generative neural network. In many cases our technique achieves a clear improvement of the performance and seems to be more robust.
  arXiv  Detail & Related papers  (2021-01-21T15:04:57Z)
• Spatially-Adaptive Pixelwise Networks for Fast Image Translation [57.359250882770525]
  We introduce a new generator architecture, aimed at fast and efficient high-resolution image-to-image translation. We use pixel-wise networks; that is, each pixel is processed independently of others. Our model is up to 18x faster than state-of-the-art baselines.
  arXiv  Detail & Related papers  (2020-12-05T10:02:03Z)
• Deep Variational Network Toward Blind Image Restoration [60.45350399661175]
  Blind image restoration is a common yet challenging problem in computer vision. We propose a novel blind image restoration method, aiming to integrate both the advantages of them. Experiments on two typical blind IR tasks, namely image denoising and super-resolution, demonstrate that the proposed method achieves superior performance over current state-of-the-arts.
  arXiv  Detail & Related papers  (2020-08-25T03:30:53Z)
• End-to-end Interpretable Learning of Non-blind Image Deblurring [102.75982704671029]
  Non-blind image deblurring is typically formulated as a linear least-squares problem regularized by natural priors on the corresponding sharp picture's gradients. We propose to precondition the Richardson solver using approximate inverse filters of the (known) blur and natural image prior kernels.
  arXiv  Detail & Related papers  (2020-07-03T15:45:01Z)
• Class-Specific Blind Deconvolutional Phase Retrieval Under a Generative Prior [8.712404218757733]
  The problem arises in various imaging modalities such as Fourier ptychography, X-ray crystallography, and in visible light communication. We propose to solve this inverse problem using alternating gradient descent algorithm under two pretrained deep generative networks as priors. The proposed recovery algorithm strives to find a sharp image and a blur kernel in the range of the respective pre-generators that textitbest explain the forward measurement model.
  arXiv  Detail & Related papers  (2020-02-28T07:36:28Z)

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.