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Equivariant and invariant deep learning models have been developed to exploit intrinsic symmetries in data, demonstrating significant effectiveness in certain scenarios. However, these methods often suffer from limited representation…
Image segmentation techniques are predominately based on parameter-laden optimization. The objective function typically involves weights for balancing competing image fidelity and segmentation regularization cost terms. Setting these…
How to extract more and useful information for single image super resolution is an imperative and difficult problem. Learning-based method is a representative method for such task. However, the results are not so stable as there may exist…
This work proposes a novel convex-non-convex formulation of the image segmentation and the image completion problems. The proposed approach is based on the minimization of a functional involving two distinct regularization terms: one…
Image reconstruction in X-ray tomography is an ill-posed inverse problem, particularly with limited available data. Regularization is thus essential, but its effectiveness hinges on the choice of a regularization parameter that balances…
A central theme in classical algorithms for the reconstruction of discontinuous functions from observational data is perimeter regularization via the use of the total variation. On the other hand, sparse or noisy data often demands a…
Building on the well-known total-variation (TV), this paper develops a general regularization technique based on nonlinear isotropic diffusion (NID) for inverse problems with piecewise smooth solutions. The novelty of our approach is to be…
In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in data analysis and machine learning. But often, images are not…
This article proposes a novel regularization method, named Geometric Spatio-Spectral Total Variation (GeoSSTV), for hyperspectral (HS) image denoising and destriping. HS images are inevitably affected by various types of noise due to the…
Total Variation (TV) based regularization has been widely applied in restoration problems due to its simple derivative filters based formulation and robust performance. While first order TV suffers from staircase effect, second order TV…
Regularization method and Bayesian inverse method are two dominating ways for solving inverse problems generated from various fields, e.g., seismic exploration and medical imaging. The two methods are related with each other by the MAP…
The problem of restoration of digital images from their degraded measurements plays a central role in a multitude of practically important applications. A particularly challenging instance of this problem occurs in the case when the…
We consider a patch-based learning approach defined in terms of neural networks to estimate spatially adaptive regularisation parameter maps for image denoising with weighted Total Variation (TV) and test it to situations when the noise…
Optimization on Riemannian manifolds widely arises in eigenvalue computation, density functional theory, Bose-Einstein condensates, low rank nearest correlation, image registration, and signal processing, etc. We propose an adaptive…
We consider inverse problems with large null spaces, which arise in important applications such as in inverse ECG and EEG procedures. Standard regularization methods typically produce solutions in or near the orthogonal complement of the…
In this paper, we propose and develop a novel nonlocal variational technique based on saturation-value similarity for color image restoration. In traditional nonlocal methods, image patches are extracted from red, green and blue channels of…
In this paper, we consider a backward problem for a time-space fractional diffusion process. For this problem, we propose to construct the initial data by minimizing data residual error in fourier space domain and variable total variation…
The importance of regularization has been well established in image reconstruction -- which is the computational inversion of imaging forward model -- with applications including deconvolution for microscopy, tomographic reconstruction,…
Recent developments in deep learning have revolutionized the paradigm of image restoration. However, its applications on real image denoising are still limited, due to its sensitivity to training data and the complex nature of real image…
In this work, we propose a new paradigm of iterative model-based reconstruction algorithms for providing real-time solution for zooming-in and refining a region of interest in medical and clinical tomographic images. This algorithmic…