5,553 research outputs found
Phase Transitions in Phase Retrieval
Consider a scenario in which an unknown signal is transformed by a known
linear operator, and then the pointwise absolute value of the unknown output
function is reported. This scenario appears in several applications, and the
goal is to recover the unknown signal -- this is called phase retrieval. Phase
retrieval has been a popular subject of research in the last few years, both in
determining whether complete information is available with a given linear
operator, and in finding efficient and stable phase retrieval algorithms in the
cases where complete information is available. Interestingly, there are a few
ways to measure information completeness, and each way appears to be governed
by a phase transition of sorts. This chapter will survey the state of the art
with some of these phase transitions, and identify a few open problems for
further research.Comment: Book chapter, survey of recent literature, submitted to Excursions in
Harmonic Analysis: The February Fourier Talks at the Norbert Wiener Cente
Gardner optimal capacity of the diluted Blume-Emery-Griffiths neural network
The optimal capacity of a diluted Blume-Emery-Griffiths neural network is
studied as a function of the pattern activity and the embedding stability using
the Gardner entropy approach. Annealed dilution is considered, cutting some of
the couplings referring to the ternary patterns themselves and some of the
couplings related to the active patterns, both simultaneously (synchronous
dilution) or independently (asynchronous dilution). Through the de
Almeida-Thouless criterion it is found that the replica-symmetric solution is
locally unstable as soon as there is dilution. The distribution of the
couplings shows the typical gap with a width depending on the amount of
dilution, but this gap persists even in cases where a particular type of
coupling plays no role in the learning process.Comment: 9 pages Latex, 2 eps figure
Euclidean Distance Matrices: Essential Theory, Algorithms and Applications
Euclidean distance matrices (EDM) are matrices of squared distances between
points. The definition is deceivingly simple: thanks to their many useful
properties they have found applications in psychometrics, crystallography,
machine learning, wireless sensor networks, acoustics, and more. Despite the
usefulness of EDMs, they seem to be insufficiently known in the signal
processing community. Our goal is to rectify this mishap in a concise tutorial.
We review the fundamental properties of EDMs, such as rank or
(non)definiteness. We show how various EDM properties can be used to design
algorithms for completing and denoising distance data. Along the way, we
demonstrate applications to microphone position calibration, ultrasound
tomography, room reconstruction from echoes and phase retrieval. By spelling
out the essential algorithms, we hope to fast-track the readers in applying
EDMs to their own problems. Matlab code for all the described algorithms, and
to generate the figures in the paper, is available online. Finally, we suggest
directions for further research.Comment: - 17 pages, 12 figures, to appear in IEEE Signal Processing Magazine
- change of title in the last revisio
Transcribing Content from Structural Images with Spotlight Mechanism
Transcribing content from structural images, e.g., writing notes from music
scores, is a challenging task as not only the content objects should be
recognized, but the internal structure should also be preserved. Existing image
recognition methods mainly work on images with simple content (e.g., text lines
with characters), but are not capable to identify ones with more complex
content (e.g., structured symbols), which often follow a fine-grained grammar.
To this end, in this paper, we propose a hierarchical Spotlight Transcribing
Network (STN) framework followed by a two-stage "where-to-what" solution.
Specifically, we first decide "where-to-look" through a novel spotlight
mechanism to focus on different areas of the original image following its
structure. Then, we decide "what-to-write" by developing a GRU based network
with the spotlight areas for transcribing the content accordingly. Moreover, we
propose two implementations on the basis of STN, i.e., STNM and STNR, where the
spotlight movement follows the Markov property and Recurrent modeling,
respectively. We also design a reinforcement method to refine the framework by
self-improving the spotlight mechanism. We conduct extensive experiments on
many structural image datasets, where the results clearly demonstrate the
effectiveness of STN framework.Comment: Accepted by KDD2018 Research Track. In proceedings of the 24th ACM
SIGKDD International Conference on Knowledge Discovery and Data Mining
(KDD'18
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