771 research outputs found
Stable image reconstruction using total variation minimization
This article presents near-optimal guarantees for accurate and robust image
recovery from under-sampled noisy measurements using total variation
minimization. In particular, we show that from O(slog(N)) nonadaptive linear
measurements, an image can be reconstructed to within the best s-term
approximation of its gradient up to a logarithmic factor, and this factor can
be removed by taking slightly more measurements. Along the way, we prove a
strengthened Sobolev inequality for functions lying in the null space of
suitably incoherent matrices.Comment: 25 page
Process of image super-resolution
In this paper we explain a process of super-resolution reconstruction
allowing to increase the resolution of an image.The need for high-resolution
digital images exists in diverse domains, for example the medical and spatial
domains. The obtaining of high-resolution digital images can be made at the
time of the shooting, but it is often synonymic of important costs because of
the necessary material to avoid such costs, it is known how to use methods of
super-resolution reconstruction, consisting from one or several low resolution
images to obtain a high-resolution image. The american patent US 9208537
describes such an algorithm. A zone of one low-resolution image is isolated and
categorized according to the information contained in pixels forming the
borders of the zone. The category of it zone determines the type of
interpolation used to add pixels in aforementioned zone, to increase the
neatness of the images. It is also known how to reconstruct a low-resolution
image there high-resolution image by using a model of super-resolution
reconstruction whose learning is based on networks of neurons and on image or a
picture library. The demand of chinese patent CN 107563965 and the scientist
publication "Pixel Recursive Super Resolution", R. Dahl, M. Norouzi, J. Shlens
propose such methods. The aim of this paper is to demonstrate that it is
possible to reconstruct coherent human faces from very degraded pixelated
images with a very fast algorithm, more faster than compressed sensing (CS),
easier to compute and without deep learning, so without important technology
resources, i.e. a large database of thousands training images (see
arXiv:2003.13063).
This technological breakthrough has been patented in 2018 with the demand of
French patent FR 1855485 (https://patents.google.com/patent/FR3082980A1, see
the HAL reference https://hal.archives-ouvertes.fr/hal-01875898v1).Comment: 19 pages, 10 figure
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