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Image restoration has witnessed significant advancements with the development of deep learning models. Transformer-based models, particularly those using window-based self-attention, have become a dominant force. However, their performance…
While deep learning-based methods for blind face restoration have achieved unprecedented success, they still suffer from two major limitations. First, most of them deteriorate when facing complex degradations out of their training data.…
A new approach of obtaining stratified random samples from statistically dependent random variables is described. The proposed method can be used to obtain samples from the input space of a computer forward model in estimating expectations…
In this paper an extension of the sparse decomposition problem is considered and an algorithm for solving it is presented. In this extension, it is known that one of the shifted versions of a signal s (not necessarily the original signal…
Scaling sequence modeling to extreme contexts requires balancing computational efficiency with representational expressivity. While Transformers provide precise retrieval via the attention mechanism, their quadratic $\mathcal{O}(T^2)$…
A typical system of k difference (or differential) equations can be compressed, or folded into a difference (or ordinary differential) equation of order k. Such foldings appear in control theory as the canonical forms of the controllability…
The use of hearing aids will increase in the coming years due to demographic change. One open problem that remains to be solved by a new generation of hearing aids is the cocktail party problem. A possible solution is…
It is well-known that zero-shot learning (ZSL) can suffer severely from the problem of domain shift, where the true and learned data distributions for the unseen classes do not match. Although transductive ZSL (TZSL) attempts to improve…
Blind ptychography is a phase retrieval method using multiple coded diffraction patterns from different, overlapping parts of the unknown extended object illuminated with an unknown window function. The window function is also known as the…
Diffusion transformers have demonstrated remarkable generation quality, albeit requiring longer training iterations and numerous inference steps. In each denoising step, diffusion transformers encode the noisy inputs to extract the…
We give a quantum algorithm for solving a shifted multiplicative character problem over Z/nZ and finite fields. We show that the algorithm can be interpreted as a matrix factorization or as solving a deconvolution problem and give…
Deep-learning (DL)-based image deconvolution (ID) has exhibited remarkable recovery performance, surpassing traditional linear methods. However, unlike traditional ID approaches that rely on analytical properties of the point spread…
This paper develops the numerical inverse scattering transform (NIST) framework for the coupled modified Korteweg-de Vries (mKdV) equation based on its associated Riemann-Hilbert problem. The coupled system gives rise to a $3\times3$…
The resolution of optical imaging is classically limited by the width of the point-spread function, which in turn is determined by the Rayleigh length. Recently, spatial-mode demultiplexing (SPADE) has been proposed as a method to achieve…
Many applications in signal processing benefit from the sparsity of signals in a certain transform domain or dictionary. Synthesis sparsifying dictionaries that are directly adapted to data have been popular in applications such as image…
We consider the model of the focusing one-dimensional nonlinear Schr\"odinger equation (fNLSE) in the presence of an unstable constant background, which exhibits coherent solitary wave structures -- breathers. Within the inverse scattering…
For audio source separation applications, it is common to estimate the magnitude of the short-time Fourier transform (STFT) of each source. In order to further synthesizing time-domain signals, it is necessary to recover the phase of the…
A new near-to-far-field transformation algorithm for three-dimensional finite-different time-domain is presented in this article. This new approach is based directly on the polarization current of the scatterer, not the scattered near…
Blind source separation (BSS) algorithms are unsupervised methods, which are the cornerstone of hyperspectral data analysis by allowing for physically meaningful data decompositions. BSS problems being ill-posed, the resolution requires…
The synthesis of string transformation programs from input-output examples utilizes various techniques, all based on an inductive bias that comprises a restricted set of basic operators to be combined. A new algorithm, Transduce, is…