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We present a new algorithm for the computation of the inverse Abel transform, a problem which emerges in many areas of physics and engineering. We prove that the Legendre coefficients of a given function coincide with the Fourier…
Modeling future traffic conditions often relies heavily on complex spatial-temporal neural networks to capture spatial and temporal correlations, which can overlook the inherent noise in the data. This noise, often manifesting as unexpected…
In this article, the problem of identifying the source term in transport processes given by a complete parabolic equation is studied mathematically from noisy measurements taken at an arbitrary fixed time. The problem is solved analytically…
We study image inverse problems with a normalizing flow prior. Our formulation views the solution as the maximum a posteriori estimate of the image conditioned on the measurements. This formulation allows us to use noise models with…
We propose an efficient and flexible method for solving Abel integral equation of the first kind, frequently appearing in many fields of astrophysics, physics, chemistry, and applied sciences. This equation represents an ill-posed problem,…
Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…
Deep Learning (DL) inversion is a promising method for real time interpretation of logging while drilling (LWD) resistivity measurements for well navigation applications. In this context, measurement noise may significantly affect inversion…
Quantum kernel methods have been widely recognized as one of promising quantum machine learning algorithms that have potential to achieve quantum advantages. In this paper, we theoretically characterize the power of noisy quantum kernels…
A new method for removing impulse noise from speech in the wavelet transform domain is proposed. The method utilizes the multiresolution property of the wavelet transform, which provides finer time resolution at the higher frequencies than…
Running quantum programs is fraught with challenges on on today's noisy intermediate scale quantum (NISQ) devices. Many of these challenges originate from the error characteristics that stem from rapid decoherence and noise during…
Diffusion-based visuomotor policies built on 3D visual representations have achieved strong performance in learning complex robotic skills. However, most existing methods employ an oversized denoising decoder. While increasing model…
Quantization is a critical step to enable efficient LLM serving under limited resource. However, previous research observes that certain weights in the LLM, known as outliers, are significantly sensitive to quantization noises. Existing…
We study two aspects of noisy computations during inference. The first aspect is how to mitigate their side effects for naturally trained deep learning systems. One of the motivations for looking into this problem is to reduce the high…
We introduce the Laplace neural operator (LNO), which leverages the Laplace transform to decompose the input space. Unlike the Fourier Neural Operator (FNO), LNO can handle non-periodic signals, account for transient responses, and exhibit…
We present a method for computing the inverse parameters and the solution field to inverse parametric PDEs based on randomized neural networks. This extends the local extreme learning machine technique originally developed for forward PDEs…
Simulating real-time dynamics under a Hamiltonian is a central goal of quantum information science. While numerous Hamiltonian-simulation quantum algorithms have been proposed, the effects of physical noise have rarely been incorporated…
Conditional stability estimates require additional regularization for obtaining stable approximate solutions if the validity area of such estimates is not completely known. In this context, we consider ill-posed nonlinear inverse problems…
Evolutionary computation can be used to optimize several different aspects of neural network architectures. For instance, the TaylorGLO method discovers novel, customized loss functions, resulting in improved performance, faster training,…
Label noise presents a real challenge for supervised learning algorithms. Consequently, mitigating label noise has attracted immense research in recent years. Noise robust losses is one of the more promising approaches for dealing with…
This paper considers the linear inverse problem where we wish to estimate a structured signal $x$ from its corrupted observations. When the problem is ill-posed, it is natural to make use of a convex function $f(\cdot)$ that exploits the…