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Implicit neural representations (INRs) have emerged as a powerful tool for solving inverse problems in computer vision and computational imaging. INRs represent images as continuous domain functions realized by a neural network taking…
Iterative deblurring, notably the Richardson-Lucy algorithm with and without regularization, is analyzed in the context of nuclear and high-energy physics applications. In these applications, probability distributions may be discretized…
The explicit low-rank regularization, e.g., nuclear norm regularization, has been widely used in imaging sciences. However, it has been found that implicit regularization outperforms explicit ones in various image processing tasks. Another…
These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads…
We present an approach to learning regular spatial transformations between image pairs in the context of medical image registration. Contrary to optimization-based registration techniques and many modern learning-based methods, we do not…
Implicit Neural Representation (INR) has emerged as an effective method for unsupervised image denoising. However, INR models are typically overparameterized; consequently, these models are prone to overfitting during learning, resulting in…
Learning-based 3D reconstruction methods have shown impressive results. However, most methods require 3D supervision which is often hard to obtain for real-world datasets. Recently, several works have proposed differentiable rendering…
Spectral measurements in the infrared (IR) optical range provide unique fingerprints of materials which are useful for material analysis, environmental sensing, and health diagnostics. Current IR spectroscopy techniques require the use of…
We consider simple bilevel optimization problems where the goal is to compute among the optimal solutions of a composite convex optimization problem, one that minimizes a secondary objective function. Our main contribution is threefold. (i)…
We deal with the solution of a generic linear inverse problem in the Hilbert space setting. The exact right hand side is unknown and only accessible through discretised measurements corrupted by white noise with unknown arbitrary…
The recent development of diffusion models has led to significant progress in solving inverse problems by leveraging these models as powerful generative priors. However, challenges persist due to the ill-posed nature of such problems, often…
We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations…
We propose a new method to calculate the 4-dimensional divergent integrals. By calculating the one loop integral as an example, the regularization of the integrals in 3-dimension momentum space are given in details. We find that the new…
The goal of this paper is to further develop an approach to inverse problems with imperfect forward operators that is based on partially ordered spaces. Studying the dual problem yields useful insights into the convergence of the…
Spectral imaging is a fundamental diagnostic technique with widespread application. Conventional spectral imaging approaches have intrinsic limitations on spatial and spectral resolutions due to the physical components they rely on. To…
Studies in string theory and quantum gravity suggest the existence of a finite lower limit $\Delta x_0$ to the possible resolution of distances, at the latest on the scale of the Planck length of $10^{-35}m$. Within the framework of the…
Representing visual signals by implicit representation (e.g., a coordinate based deep network) has prevailed among many vision tasks. This work explores a new intriguing direction: training a stylized implicit representation, using a…
There is currently a high demand for theoretical predictions for processes at next-to-next-to-leading order (NNLO) and beyond, mainly due to the large amount of data which has already been collected at LHC. This requires practical methods…
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…
Infrared optical photonic crystals fabricated using direct laser writing, which is based on the two-photon polymerization of suitable monomers, have received substantial interest since the emergence of this process. Two-photon…