21,726 research outputs found
Direct probing of the Wigner function by time-multiplexed detection of photon statistics
We investigate the capabilities of loss-tolerant quantum state
characterization using a photon-number resolving, time-multiplexed detector
(TMD). We employ the idea of probing the Wigner function point-by-point in
phase space via photon parity measurements and displacement operations,
replacing the conventional homodyne tomography. Our emphasis lies on
reconstructing the Wigner function of non-Gaussian Fock states with highly
negative values in a scheme that is based on a realistic experimental setup. In
order to establish the concept of loss-tolerance for state characterization we
show how losses can be decoupled from the impact of other experimental
imperfections, i.e. the non-unity transmittance of the displacement
beamsplitter and non-ideal mode overlap. We relate the experimentally
accessible parameters to effective ones that are needed for an optimised state
reconstruction. The feasibility of our approach is tested by Monte Carlo
simulations, which provide bounds resulting from statistical errors that are
due to limited data sets. Our results clearly show that high losses can be
accepted for a defined parameter range, and moreover, that (in contrast to
homodyne detection) mode mismatch results in a distinct signature, which can be
evaluated by analysing the photon number oscillations of the displaced Fock
states.Comment: 22 pages, 13 figures, published versio
Role of anticausal inverses in multirate filter-banks. I. System-theoretic fundamentals
In a maximally decimated filter bank with identical decimation ratios for all channels, the perfect reconstructibility property and the nature of reconstruction filters (causality, stability, FIR property, and so on) depend on the properties of the polyphase matrix. Various properties and capabilities of the filter bank depend on the properties of the polyphase matrix as well as the nature of its inverse. In this paper we undertake a study of the types of inverses and characterize them according to their system theoretic properties (i.e., properties of state-space descriptions, McMillan degree, degree of determinant, and so forth). We find in particular that causal polyphase matrices with anticausal inverses have an important role in filter bank theory. We study their properties both for the FIR and IIR cases. Techniques for implementing anticausal IIR inverses based on state space descriptions are outlined. It is found that causal FIR matrices with anticausal FIR inverses (cafacafi) have a key role in the characterization of FIR filter banks. In a companion paper, these results are applied for the factorization of biorthogonal FIR filter banks, and a generalization of the lapped orthogonal transform called the biorthogonal lapped transform (BOLT) developed
Distributed soft thresholding for sparse signal recovery
In this paper, we address the problem of distributed sparse recovery of
signals acquired via compressed measurements in a sensor network. We propose a
new class of distributed algorithms to solve Lasso regression problems, when
the communication to a fusion center is not possible, e.g., due to
communication cost or privacy reasons. More precisely, we introduce a
distributed iterative soft thresholding algorithm (DISTA) that consists of
three steps: an averaging step, a gradient step, and a soft thresholding
operation. We prove the convergence of DISTA in networks represented by regular
graphs, and we compare it with existing methods in terms of performance,
memory, and complexity.Comment: Revised version. Main improvements: extension of the convergence
theorem to regular graphs; new numerical results and comparisons with other
algorithm
Semantic Photo Manipulation with a Generative Image Prior
Despite the recent success of GANs in synthesizing images conditioned on
inputs such as a user sketch, text, or semantic labels, manipulating the
high-level attributes of an existing natural photograph with GANs is
challenging for two reasons. First, it is hard for GANs to precisely reproduce
an input image. Second, after manipulation, the newly synthesized pixels often
do not fit the original image. In this paper, we address these issues by
adapting the image prior learned by GANs to image statistics of an individual
image. Our method can accurately reconstruct the input image and synthesize new
content, consistent with the appearance of the input image. We demonstrate our
interactive system on several semantic image editing tasks, including
synthesizing new objects consistent with background, removing unwanted objects,
and changing the appearance of an object. Quantitative and qualitative
comparisons against several existing methods demonstrate the effectiveness of
our method.Comment: SIGGRAPH 201
Performance of Linear Field Reconstruction Techniques with Noise and Uncertain Sensor Locations
We consider a wireless sensor network, sampling a bandlimited field,
described by a limited number of harmonics. Sensor nodes are irregularly
deployed over the area of interest or subject to random motion; in addition
sensors measurements are affected by noise. Our goal is to obtain a high
quality reconstruction of the field, with the mean square error (MSE) of the
estimate as performance metric. In particular, we analytically derive the
performance of several reconstruction/estimation techniques based on linear
filtering. For each technique, we obtain the MSE, as well as its asymptotic
expression in the case where the field number of harmonics and the number of
sensors grow to infinity, while their ratio is kept constant. Through numerical
simulations, we show the validity of the asymptotic analysis, even for a small
number of sensors. We provide some novel guidelines for the design of sensor
networks when many parameters, such as field bandwidth, number of sensors,
reconstruction quality, sensor motion characteristics, and noise level of the
measures, have to be traded off
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