ﻻ يوجد ملخص باللغة العربية
We introduce a Prony-like method to recover a continuous domain 2-D piecewise smooth image from few of its Fourier samples. Assuming the discontinuity set of the image is localized to the zero level-set of a trigonometric polynomial, we show the Fourier transform coefficients of partial derivatives of the signal satisfy an annihilation relation. We present necessary and sufficient conditions for unique recovery of piecewise constant images using the above annihilation relation. We pose the recovery of the Fourier coefficients of the signal from the measurements as a convex matrix completion algorithm, which relies on the lifting of the Fourier data to a structured low-rank matrix; this approach jointly estimates the signal and the annihilating filter. Finally, we demonstrate our algorithm on the recovery of MRI phantoms from few low-resolution Fourier samples.
We introduce a method to recover a continuous domain representation of a piecewise constant two-dimensional image from few low-pass Fourier samples. Assuming the edge set of the image is localized to the zero set of a trigonometric polynomial, we sho
With the tremendous advances of Convolutional Neural Networks (ConvNets) on object recognition, we can now obtain reliable enough machine-labeled annotations easily by predictions from off-the-shelf ConvNets. In this work, we present an abstraction m
We propose pixelNeRF, a learning framework that predicts a continuous neural scene representation conditioned on one or few input images. The existing approach for constructing neural radiance fields involves optimizing the representation to every sc
In this paper, we aim to create generalizable and controllable neural signed distance fields (SDFs) that represent clothed humans from monocular depth observations. Recent advances in deep learning, especially neural implicit representations, have en
Given any $f$ a locally finitely piecewise affine homeomorphism of $Omega subset rn$ onto $Delta subset rn$ in $W^{1,p}$, $1leq p < infty$ and any $epsilon >0$ we construct a smooth injective map $tilde{f}$ such that $|f-tilde{f}|_{W^{1,p}(Omega,rn)} < epsilon$.