22,413 research outputs found
Better than a lens -- Increasing the signal-to-noise ratio through pupil splitting
Lenses are designed to fulfill Fermats principle such that all light
interferes constructively in its focus, guaranteeing its maximum concentration.
It can be shown that imaging via an unmodified full pupil yields the maximum
transfer strength for all spatial frequencies transferable by the system.
Seemingly also the signal-to-noise ratio (SNR) is optimal. The achievable SNR
at a given photon budget is critical especially if that budget is strictly
limited as in the case of fluorescence microscopy. In this work we propose a
general method which achieves a better SNR for high spatial frequency
information of an optical imaging system, without the need to capture more
photons. This is achieved by splitting the pupil of an incoherent imaging
system such that two (or more) sub-images are simultaneously acquired and
computationally recombined. We compare the theoretical performance of split
pupil imaging to the non-split scenario and implement the splitting using a
tilted elliptical mirror placed at the back-focal-plane (BFP) of a fluorescence
widefield microscope
Quantifying Uncertainty in High Dimensional Inverse Problems by Convex Optimisation
Inverse problems play a key role in modern image/signal processing methods.
However, since they are generally ill-conditioned or ill-posed due to lack of
observations, their solutions may have significant intrinsic uncertainty.
Analysing and quantifying this uncertainty is very challenging, particularly in
high-dimensional problems and problems with non-smooth objective functionals
(e.g. sparsity-promoting priors). In this article, a series of strategies to
visualise this uncertainty are presented, e.g. highest posterior density
credible regions, and local credible intervals (cf. error bars) for individual
pixels and superpixels. Our methods support non-smooth priors for inverse
problems and can be scaled to high-dimensional settings. Moreover, we present
strategies to automatically set regularisation parameters so that the proposed
uncertainty quantification (UQ) strategies become much easier to use. Also,
different kinds of dictionaries (complete and over-complete) are used to
represent the image/signal and their performance in the proposed UQ methodology
is investigated.Comment: 5 pages, 5 figure
Revisiting parton evolution and the large-x limit
This remark is part of an ongoing project to simplify the structure of the
multi-loop anomalous dimensions for parton distributions and fragmentation
functions. It answers the call for a "structural explanation" of a "very
suggestive" relation found by Moch, Vermaseren and Vogt in the context of the
x->1 behaviour of three-loop DIS anomalous dimensions. It also highlights
further structure that remains to be fully explained.Comment: 6 pages, v2 corrects misprints and contains an additional referenc
PURIFY: a new algorithmic framework for next-generation radio-interferometric imaging
In recent works, compressed sensing (CS) and convex opti- mization techniques have been applied to radio-interferometric imaging showing the potential to outperform state-of-the-art imaging algorithms in the field. We review our latest contributions [1, 2, 3], which leverage the versatility of convex optimization to both handle realistic continuous visibilities and offer a highly parallelizable structure paving the way to significant acceleration of the reconstruction and high-dimensional data scalability. The new algorithmic structure promoted in a new software PURIFY (beta version) relies on the simultaneous-direction method of multipliers (SDMM). The performance of various sparsity priors is evaluated through simulations in the continuous visibility setting, confirming the superiority of our recent average sparsity approach SARA
Discriminative Transfer Learning for General Image Restoration
Recently, several discriminative learning approaches have been proposed for
effective image restoration, achieving convincing trade-off between image
quality and computational efficiency. However, these methods require separate
training for each restoration task (e.g., denoising, deblurring, demosaicing)
and problem condition (e.g., noise level of input images). This makes it
time-consuming and difficult to encompass all tasks and conditions during
training. In this paper, we propose a discriminative transfer learning method
that incorporates formal proximal optimization and discriminative learning for
general image restoration. The method requires a single-pass training and
allows for reuse across various problems and conditions while achieving an
efficiency comparable to previous discriminative approaches. Furthermore, after
being trained, our model can be easily transferred to new likelihood terms to
solve untrained tasks, or be combined with existing priors to further improve
image restoration quality
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