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Let $K$ denote a field and let $V$ denote a vector space over $K$ with finite positive dimension. We consider a pair of linear transformations $A:V\to V$ and $A^*:V\to V$ that satisfy both conditions below: (i) There exists a basis for $V$…

We study a new family of inverse problems for recovering representations of corrupted data. We assume access to a pre-trained representation learning network R(x) that operates on clean images, like CLIP. The problem is to recover the…

The results on the inversion of convolution operators as well as Toeplitz (and block Toeplitz) matrices in the $1$-D (one-dimensional) case are classical and have numerous applications. Last year, we considered the $2$-D case of…

We study the Jordan frame formulation of generalizations of scalar-tensor theories conceived by replacing the scalar with other fields such as vectors. The generic theory in this family contains higher order time derivative terms in the…

Most algorithms constructing bases of finite-dimensional vector spaces return basis vectors which, apart from orthogonality, do not show any special properties. While every basis is sufficient to define the vector space, not all bases are…

For finite dimensional CMV matrices the classical inverse spectral problems are considered. We solve the inverse problem of reconstructing a CMV matrix by its Weyl's function, the problem of reconstructing the matrix by two spectra of CMV…

This work introduces a general numerical technique to invert one dimensional analytic or tabulated nonlinear functions in assigned ranges of interest. The proposed approach is based on an optimal version of the k-vector range searching, an…

To edit a real photo using Generative Adversarial Networks (GANs), we need a GAN inversion algorithm to identify the latent vector that perfectly reproduces it. Unfortunately, whereas existing inversion algorithms can synthesize images…

The widespread use of vector graphics creates a significant demand for vectorization methods. While recent learning-based techniques have shown their capability to create vector images of clear topology, filling these primitives with…

We consider the problem of 3D shape recovery from ultra-fast motion-blurred images. While 3D reconstruction from static images has been extensively studied, recovering geometry from extreme motion-blurred images remains challenging. Such…

We present a topology-informed inverse rendering approach for reconstructing high-genus surface meshes from multi-view images. Compared to 3D representations like voxels and point clouds, mesh-based representations are preferred as they…

Pretrained segmentation models for cardiac magnetic resonance imaging (MRI) struggle to generalize across different imaging sequences due to significant variations in image contrast. These variations arise from changes in imaging protocols,…

In this paper a semi-supervised deep framework is proposed for the problem of 3D shape inverse rendering from a single 2D input image. The main structure of proposed framework consists of unsupervised pre-trained components which…

Let $\mathcal R$ denote the generalized Radon transform (GRT), which integrates over a family of $N$-dimensional smooth submanifolds $\mathcal S_{\tilde y}\subset\mathcal U$, $1\le N\le n-1$, where an open set $\mathcal U\subset\mathbb R^n$…

We consider the tomography problem of recovering a covector field on a simple Riemannian manifold based on its weighted Doppler transformation over a family of curves $\Gamma$. This is a generalization of the attenuated Doppler transform.…

We discuss the local behaviour of vector fields in the plane $\R^2$ around a regular singular point, using recently introduced reduced normal forms, i.e. Poincar\'e and Lie renormalized forms [{\it Lett. Math. Phys.} {\bf 42} (1997),…

This paper presents an easy-to-control volume peeling method for multi-axis machining based on the computation taken on vector fields. The current scalar field based methods are not flexible and the vector-field based methods do not…

We use singular value decomposition techniques to generalize the wavelet transform modulus maxima method to the multifractal analysis of vector-valued random fields. The method is calibrated on synthetic multifractal 2D vector measures and…

Numerous techniques have been proposed for reconstructing 3D models for opaque objects in past decades. However, none of them can be directly applied to transparent objects. This paper presents a fully automatic approach for reconstructing…

Recovering microscopic couplings directly from data provides a route to solving the inverse problem in statistical field theories, one that complements the traditional-often computationally intractable-forward approach of predicting…