806 research outputs found
Poisson noise reduction with non-local PCA
Photon-limited imaging arises when the number of photons collected by a
sensor array is small relative to the number of detector elements. Photon
limitations are an important concern for many applications such as spectral
imaging, night vision, nuclear medicine, and astronomy. Typically a Poisson
distribution is used to model these observations, and the inherent
heteroscedasticity of the data combined with standard noise removal methods
yields significant artifacts. This paper introduces a novel denoising algorithm
for photon-limited images which combines elements of dictionary learning and
sparse patch-based representations of images. The method employs both an
adaptation of Principal Component Analysis (PCA) for Poisson noise and recently
developed sparsity-regularized convex optimization algorithms for
photon-limited images. A comprehensive empirical evaluation of the proposed
method helps characterize the performance of this approach relative to other
state-of-the-art denoising methods. The results reveal that, despite its
conceptual simplicity, Poisson PCA-based denoising appears to be highly
competitive in very low light regimes.Comment: erratum: Image man is wrongly name pepper in the journal versio
Compressed sensing performance bounds under Poisson noise
This paper describes performance bounds for compressed sensing (CS) where the
underlying sparse or compressible (sparsely approximable) signal is a vector of
nonnegative intensities whose measurements are corrupted by Poisson noise. In
this setting, standard CS techniques cannot be applied directly for several
reasons. First, the usual signal-independent and/or bounded noise models do not
apply to Poisson noise, which is non-additive and signal-dependent. Second, the
CS matrices typically considered are not feasible in real optical systems
because they do not adhere to important constraints, such as nonnegativity and
photon flux preservation. Third, the typical -- minimization
leads to overfitting in the high-intensity regions and oversmoothing in the
low-intensity areas. In this paper, we describe how a feasible positivity- and
flux-preserving sensing matrix can be constructed, and then analyze the
performance of a CS reconstruction approach for Poisson data that minimizes an
objective function consisting of a negative Poisson log likelihood term and a
penalty term which measures signal sparsity. We show that, as the overall
intensity of the underlying signal increases, an upper bound on the
reconstruction error decays at an appropriate rate (depending on the
compressibility of the signal), but that for a fixed signal intensity, the
signal-dependent part of the error bound actually grows with the number of
measurements or sensors. This surprising fact is both proved theoretically and
justified based on physical intuition.Comment: 12 pages, 3 pdf figures; accepted for publication in IEEE
Transactions on Signal Processin
Detecting Unspecified Structure in Low-Count Images
Unexpected structure in images of astronomical sources often presents itself
upon visual inspection of the image, but such apparent structure may either
correspond to true features in the source or be due to noise in the data. This
paper presents a method for testing whether inferred structure in an image with
Poisson noise represents a significant departure from a baseline (null) model
of the image. To infer image structure, we conduct a Bayesian analysis of a
full model that uses a multiscale component to allow flexible departures from
the posited null model. As a test statistic, we use a tail probability of the
posterior distribution under the full model. This choice of test statistic
allows us to estimate a computationally efficient upper bound on a p-value that
enables us to draw strong conclusions even when there are limited computational
resources that can be devoted to simulations under the null model. We
demonstrate the statistical performance of our method on simulated images.
Applying our method to an X-ray image of the quasar 0730+257, we find
significant evidence against the null model of a single point source and
uniform background, lending support to the claim of an X-ray jet
3D Target Detection and Spectral Classification for Single-photon LiDAR Data
3D single-photon LiDAR imaging has an important role in many applications.
However, full deployment of this modality will require the analysis of low
signal to noise ratio target returns and a very high volume of data. This is
particularly evident when imaging through obscurants or in high ambient
background light conditions. This paper proposes a multiscale approach for 3D
surface detection from the photon timing histogram to permit a significant
reduction in data volume. The resulting surfaces are background-free and can be
used to infer depth and reflectivity information about the target. We
demonstrate this by proposing a hierarchical Bayesian model for 3D
reconstruction and spectral classification of multispectral single-photon LiDAR
data. The reconstruction method promotes spatial correlation between
point-cloud estimates and uses a coordinate gradient descent algorithm for
parameter estimation. Results on simulated and real data show the benefits of
the proposed target detection and reconstruction approaches when compared to
state-of-the-art processing algorithm
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