Diffusion models can learn strong image priors from underlying data distribution and use them to solve inverse problems, but the training process is computationally expensive and requires lots of data. Such bottlenecks prevent most existing works from being feasible for high-dimensional and high-resolution data such as 3D images. This paper proposes a method to learn an efficient data prior for the entire image by training diffusion models only on patches of images. Specifically, we propose a patch-based position-aware diffusion inverse solver, called PaDIS, where we obtain the score function of the whole image through scores of patches and their positional encoding and utilize this as the prior for solving inverse problems. First of all, we show that this diffusion model achieves an improved memory efficiency and data efficiency while still maintaining the capability to generate entire images via positional encoding. Additionally, the proposed PaDIS model is highly flexible and can be plugged in with different diffusion inverse solvers (DIS). We demonstrate that the proposed PaDIS approach enables solving various inverse problems in both natural and medical image domains, including CT reconstruction, deblurring, and superresolution, given only patch-based priors. Notably, PaDIS outperforms previous DIS methods trained on entire image priors in the case of limited training data, demonstrating the data efficiency of our proposed approach by learning patch-based prior.
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Center for Applied Scientific Computing（应用科学计算中心）
Solving inverse problems continues to be a challenge in a wide array of applications ranging from deblurring, image inpainting, source separation etc. Most existing techniques solve such inverse problems by either explicitly or implicitly finding the inverse of the model. The former class of techniques require explicit knowledge of the measurement process which can be unrealistic, and rely on strong analytical regularizers to constrain the solution space, which often do not generalize well. The latter approaches have had remarkable success in part due to deep learning, but require a large coll…
Technion – Israel Institute of Technology（以色列理工学院）
Recent work in image processing suggests that operating on (overlapping) patches in an image may lead to state-of-the-art results. This has been demonstrated for a variety of problems including denoising, inpainting, deblurring, and super-resolution. The work reported in [1,2] takes an extra step forward by showing that ordering these patches to form an approximate shortest path can be leveraged for better processing. The core idea is to apply a simple filter on the resulting 1D smoothed signal obtained after the patch-permutation. This idea has been also explored in combination with a wavelet…
The primary issue in inverse halftoning is removing noisy dots on flat areas and restoring image structures (e.g., lines, patterns) on textured areas. Hence, a new structure-aware deep convolutional neural network that incorporates two subnetworks is proposed in this paper. One subnetwork is for image structure prediction while the other is for continuous-tone image reconstruction. First, to predict image structures, patch pairs comprising continuous-tone patches and the corresponding halftoned patches generated through digital halftoning are trained. Subsequently, gradient patches are generat…
Inner Mongolia University（内蒙古大学）；University of Hong Kong（香港大学）
Non-local self-similarity based low rank algorithms are the state-of-the-art methods for image denoising. In this paper, a new method is proposed by solving two issues: how to improve similar patches matching accuracy and build an appropriate low rank matrix approximation model for Gaussian noise. For the first issue, similar patches can be found locally or globally. Local patch matching is to find similar patches in a large neighborhood which can alleviate noise effect, but the number of patches may be insufficient. Global patch matching is to determine enough similar patches but the error ra…
GIK Institute of Engineering Sciences and Technology（GIK工程科学与技术学院）
Among the patch-based image denoising processing methods, smooth ordering of local patches (patch ordering) has been shown to give state-of-art results. For image denoising the patch ordering method forms two large TSPs (Traveling Salesman Problem) comprised of nodes in N-dimensional space. Ten approximate solutions of the two large TSPs are then used in a filtering process to form the reconstructed image. Use of large TSPs makes patch ordering a computationally intensive method. A modified patch ordering method for image denoising is proposed. In the proposed method, several smaller-sized TSP…
University of Michigan（密歇根大学）；United Imaging Research Institute of Intelligent Imaging（联影智能影像研究院）；Imperial College London（伦敦帝国理工学院）
This paper reports a CPU-level real-time stereo matching method for surgical images (10 Hz on 640 * 480 image with a single core of i5-9400). The proposed method is built on the fast ''dense inverse searching'' algorithm, which estimates the disparity of the stereo images. The overlapping image patches (arbitrary squared image segment) from the images at different scales are aligned based on the photometric consistency presumption. We propose a Bayesian framework to evaluate the probability of the optimized patch disparity at different scales. Moreover, we introduce a spatial Gaussian mixed pr…
KAIST (Korea Advanced Institute of Science and Technology)（韩国科学技术院）
In the field of 3D perception using 3D LiDAR sensors, ground segmentation is an essential task for various purposes, such as traversable area detection and object recognition. Under these circumstances, several ground segmentation methods have been proposed. However, some limitations are still encountered. First, some ground segmentation methods require fine-tuning of parameters depending on the surroundings, which is excessively laborious and time-consuming. Moreover, even if the parameters are well adjusted, a partial under-segmentation problem can still emerge, which implies ground segmenta…
University of Minnesota（明尼苏达大学）；Ecole Polytechnique（巴黎综合理工学院）
A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the proposed framework with structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared to traditional sparse inverse problem techniques. This interpretation also suggests an effective dictionary motivated initialization for the MAP-EM algorithm. We demonstrate that in a number of image …
University of Texas at Austin（德克萨斯大学奥斯汀分校）；Google Research（谷歌研究院）
We introduce a novel framework for solving inverse problems using NeRF-style generative models. We are interested in the problem of 3-D scene reconstruction given a single 2-D image and known camera parameters. We show that naively optimizing the latent space leads to artifacts and poor novel view rendering. We attribute this problem to volume obstructions that are clear in the 3-D geometry and become visible in the renderings of novel views. We propose a novel radiance field regularization method to obtain better 3-D surfaces and improved novel views given single view observations. Our method…
The non-local self-similarity property of natural images has been exploited extensively for solving various image processing problems. When it comes to video sequences, harnessing this force is even more beneficial due to the temporal redundancy. In the context of image and video denoising, many classically-oriented algorithms employ self-similarity, splitting the data into overlapping patches, gathering groups of similar ones and processing these together somehow. With the emergence of convolutional neural networks (CNN), the patch-based framework has been abandoned. Most CNN denoisers operat…
Rice University（莱斯大学）；Indian Institute of Technology (IIT) Madras（印度理工学院马德拉斯分校）；Insight Centre for Data Analytics（数据 analytics 洞察中心）
Signal reconstruction is a challenging aspect of computational imaging as it often involves solving ill-posed inverse problems. Recently, deep feed-forward neural networks have led to state-of-the-art results in solving various inverse imaging problems. However, being task specific, these networks have to be learned for each inverse problem. On the other hand, a more flexible approach would be to learn a deep generative model once and then use it as a signal prior for solving various inverse problems. We show that among the various state of the art deep generative models, autoregressive models…
Instituto de Telecomunicações（电信研究所）；Instituto Superior Técnico, University of Lisbon（里斯本大学高等技术学院）
This paper introduces a new approach to patch-based image restoration based on external datasets and importance sampling. The Minimum Mean Squared Error (MMSE) estimate of the image patches, the computation of which requires solving a multidimensional (typically intractable) integral, is approximated using samples from an external dataset. The new method, which can be interpreted as a generalization of the external non-local means (NLM), uses self-normalized importance sampling to efficiently approximate the MMSE estimates. The use of self-normalized importance sampling endows the proposed met…
End-to-end deep neural networks (DNNs) have become the state-of-the-art (SOTA) for solving inverse problems. Despite their outstanding performance, during deployment, such networks are sensitive to minor variations in the testing pipeline and often fail to reconstruct small but important details, a feature critical in medical imaging, astronomy, or defence. Such instabilities in DNNs can be explained by the fact that they ignore the forward measurement model during deployment, and thus fail to enforce consistency between their output and the input measurements. To overcome this, we propose a f…
