273 research outputs found
A Geometrical Study of Matching Pursuit Parametrization
This paper studies the effect of discretizing the parametrization of a
dictionary used for Matching Pursuit decompositions of signals. Our approach
relies on viewing the continuously parametrized dictionary as an embedded
manifold in the signal space on which the tools of differential (Riemannian)
geometry can be applied. The main contribution of this paper is twofold. First,
we prove that if a discrete dictionary reaches a minimal density criterion,
then the corresponding discrete MP (dMP) is equivalent in terms of convergence
to a weakened hypothetical continuous MP. Interestingly, the corresponding
weakness factor depends on a density measure of the discrete dictionary.
Second, we show that the insertion of a simple geometric gradient ascent
optimization on the atom dMP selection maintains the previous comparison but
with a weakness factor at least two times closer to unity than without
optimization. Finally, we present numerical experiments confirming our
theoretical predictions for decomposition of signals and images on regular
discretizations of dictionary parametrizations.Comment: 26 pages, 8 figure
Natural Image Noise Dataset
Convolutional neural networks have been the focus of research aiming to solve
image denoising problems, but their performance remains unsatisfactory for most
applications. These networks are trained with synthetic noise distributions
that do not accurately reflect the noise captured by image sensors. Some
datasets of clean-noisy image pairs have been introduced but they are usually
meant for benchmarking or specific applications. We introduce the Natural Image
Noise Dataset (NIND), a dataset of DSLR-like images with varying levels of ISO
noise which is large enough to train models for blind denoising over a wide
range of noise. We demonstrate a denoising model trained with the NIND and show
that it significantly outperforms BM3D on ISO noise from unseen images, even
when generalizing to images from a different type of camera. The Natural Image
Noise Dataset is published on Wikimedia Commons such that it remains open for
curation and contributions. We expect that this dataset will prove useful for
future image denoising applications.Comment: NTIRE at CVPR 201
Consistent Basis Pursuit for Signal and Matrix Estimates in Quantized Compressed Sensing
This paper focuses on the estimation of low-complexity signals when they are
observed through uniformly quantized compressive observations. Among such
signals, we consider 1-D sparse vectors, low-rank matrices, or compressible
signals that are well approximated by one of these two models. In this context,
we prove the estimation efficiency of a variant of Basis Pursuit Denoise,
called Consistent Basis Pursuit (CoBP), enforcing consistency between the
observations and the re-observed estimate, while promoting its low-complexity
nature. We show that the reconstruction error of CoBP decays like
when all parameters but are fixed. Our proof is connected to recent bounds
on the proximity of vectors or matrices when (i) those belong to a set of small
intrinsic "dimension", as measured by the Gaussian mean width, and (ii) they
share the same quantized (dithered) random projections. By solving CoBP with a
proximal algorithm, we provide some extensive numerical observations that
confirm the theoretical bound as is increased, displaying even faster error
decay than predicted. The same phenomenon is observed in the special, yet
important case of 1-bit CS.Comment: Keywords: Quantized compressed sensing, quantization, consistency,
error decay, low-rank, sparsity. 10 pages, 3 figures. Note abbout this
version: title change, typo corrections, clarification of the context, adding
a comparison with BPD
Ball 3D Localization From A Single Calibrated Image
Ball 3D localization in team sports has various applications including
automatic offside detection in soccer, or shot release localization in
basketball. Today, this task is either resolved by using expensive multi-views
setups, or by restricting the analysis to ballistic trajectories. In this work,
we propose to address the task on a single image from a calibrated monocular
camera by estimating ball diameter in pixels and use the knowledge of real ball
diameter in meters. This approach is suitable for any game situation where the
ball is (even partly) visible. To achieve this, we use a small neural network
trained on image patches around candidates generated by a conventional ball
detector. Besides predicting ball diameter, our network outputs the confidence
of having a ball in the image patch. Validations on 3 basketball datasets
reveals that our model gives remarkable predictions on ball 3D localization. In
addition, through its confidence output, our model improves the detection rate
by filtering the candidates produced by the detector. The contributions of this
work are (i) the first model to address 3D ball localization on a single image,
(ii) an effective method for ball 3D annotation from single calibrated images,
(iii) a high quality 3D ball evaluation dataset annotated from a single
viewpoint. In addition, the code to reproduce this research is be made freely
available at https://github.com/gabriel-vanzandycke/deepsport.Comment: 9 pages, CVSports202
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