9,805 research outputs found
WaveDM: Wavelet-Based Diffusion Models for Image Restoration
Latest diffusion-based methods for many image restoration tasks outperform
traditional models, but they encounter the long-time inference problem. To
tackle it, this paper proposes a Wavelet-Based Diffusion Model (WaveDM) with an
Efficient Conditional Sampling (ECS) strategy. WaveDM learns the distribution
of clean images in the wavelet domain conditioned on the wavelet spectrum of
degraded images after wavelet transform, which is more time-saving in each step
of sampling than modeling in the spatial domain. In addition, ECS follows the
same procedure as the deterministic implicit sampling in the initial sampling
period and then stops to predict clean images directly, which reduces the
number of total sampling steps to around 5. Evaluations on four benchmark
datasets including image raindrop removal, defocus deblurring, demoir\'eing,
and denoising demonstrate that WaveDM achieves state-of-the-art performance
with the efficiency that is comparable to traditional one-pass methods and over
100 times faster than existing image restoration methods using vanilla
diffusion models
CT Image Reconstruction by Spatial-Radon Domain Data-Driven Tight Frame Regularization
This paper proposes a spatial-Radon domain CT image reconstruction model
based on data-driven tight frames (SRD-DDTF). The proposed SRD-DDTF model
combines the idea of joint image and Radon domain inpainting model of
\cite{Dong2013X} and that of the data-driven tight frames for image denoising
\cite{cai2014data}. It is different from existing models in that both CT image
and its corresponding high quality projection image are reconstructed
simultaneously using sparsity priors by tight frames that are adaptively
learned from the data to provide optimal sparse approximations. An alternative
minimization algorithm is designed to solve the proposed model which is
nonsmooth and nonconvex. Convergence analysis of the algorithm is provided.
Numerical experiments showed that the SRD-DDTF model is superior to the model
by \cite{Dong2013X} especially in recovering some subtle structures in the
images
Image Restoration: A General Wavelet Frame Based Model and Its Asymptotic Analysis
Image restoration is one of the most important areas in imaging science.
Mathematical tools have been widely used in image restoration, where wavelet
frame based approach is one of the successful examples. In this paper, we
introduce a generic wavelet frame based image restoration model, called the
"general model", which includes most of the existing wavelet frame based models
as special cases. Moreover, the general model also includes examples that are
new to the literature. Motivated by our earlier studies [1-3], We provide an
asymptotic analysis of the general model as image resolution goes to infinity,
which establishes a connection between the general model in discrete setting
and a new variatonal model in continuum setting. The variational model also
includes some of the existing variational models as special cases, such as the
total generalized variational model proposed by [4]. In the end, we introduce
an algorithm solving the general model and present one numerical simulation as
an example
Wavelet/shearlet hybridized neural networks for biomedical image restoration
Recently, new programming paradigms have emerged that combine parallelism and numerical computations with algorithmic differentiation. This approach allows for the hybridization of neural network techniques for inverse imaging problems with more traditional methods such as wavelet-based sparsity modelling techniques. The benefits are twofold: on the one hand traditional methods with well-known properties can be integrated in neural networks, either as separate layers or tightly integrated in the network, on the other hand, parameters in traditional methods can be trained end-to-end from datasets in a neural network "fashion" (e.g., using Adagrad or Adam optimizers). In this paper, we explore these hybrid neural networks in the context of shearlet-based regularization for the purpose of biomedical image restoration. Due to the reduced number of parameters, this approach seems a promising strategy especially when dealing with small training data sets
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