2,447 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
Skellam shrinkage: Wavelet-based intensity estimation for inhomogeneous Poisson data
The ubiquity of integrating detectors in imaging and other applications
implies that a variety of real-world data are well modeled as Poisson random
variables whose means are in turn proportional to an underlying vector-valued
signal of interest. In this article, we first show how the so-called Skellam
distribution arises from the fact that Haar wavelet and filterbank transform
coefficients corresponding to measurements of this type are distributed as sums
and differences of Poisson counts. We then provide two main theorems on Skellam
shrinkage, one showing the near-optimality of shrinkage in the Bayesian setting
and the other providing for unbiased risk estimation in a frequentist context.
These results serve to yield new estimators in the Haar transform domain,
including an unbiased risk estimate for shrinkage of Haar-Fisz
variance-stabilized data, along with accompanying low-complexity algorithms for
inference. We conclude with a simulation study demonstrating the efficacy of
our Skellam shrinkage estimators both for the standard univariate wavelet test
functions as well as a variety of test images taken from the image processing
literature, confirming that they offer substantial performance improvements
over existing alternatives.Comment: 27 pages, 8 figures, slight formatting changes; submitted for
publicatio
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
Hyperspectral reconstruction in biomedical imaging using terahertz systems
Terahertz time-domain spectroscopy (THz-TDS) is an emerging modality for biomedical imaging. It is non-ionizing and can detect differences between water content and tissue density, but the detectors are rather expensive and the scan time tends to be long. Recently, it has been shown that the compressed sensing theory can lead to a radical re-design of the imaging system with lower detector cost and shorter scan time, in exchange for computation in the image reconstruction. We show in this paper that it is in fact possible to make use of the multi-frequency nature of the terahertz pulse to achieve hyperspectral reconstruction. Through effective use of the spatial sparsity, spectroscopic phase information, and correlations across the hyperspectral bands, our method can significantly improve the reconstructed image quality. This is demonstrated through using a set of experimental THz data captured in a single-pixel terahertz system. ©2010 IEEE.published_or_final_versionThe IEEE International Symposium on Circuits and Systems: Nano-Bio Circuit Fabrics and Systems (ISCAS 2010), Pars, France, 30 May-2 June 2010. In Proceedings of ISCAS, 2010, p. 2079-208
Hyperspectral reconstruction in biomedical imaging using terahertz systems
Terahertz time-domain spectroscopy (THz-TDS) is an emerging modality for biomedical imaging. It is non-ionizing and can detect differences between water content and tissue density, but the detectors are rather expensive and the scan time tends to be long. Recently, it has been shown that the compressed sensing theory can lead to a radical re-design of the imaging system with lower detector cost and shorter scan time, in exchange for computation in the image reconstruction. We show in this paper that it is in fact possible to make use of the multi-frequency nature of the terahertz pulse to achieve hyperspectral reconstruction. Through effective use of the spatial sparsity, spectroscopic phase information, and correlations across the hyperspectral bands, our method can significantly improve the reconstructed image quality. This is demonstrated through using a set of experimental THz data captured in a single-pixel terahertz system. ©2010 IEEE.published_or_final_versionThe IEEE International Symposium on Circuits and Systems: Nano-Bio Circuit Fabrics and Systems (ISCAS 2010), Pars, France, 30 May-2 June 2010. In Proceedings of ISCAS, 2010, p. 2079-208
Singleshot polychromatic coherent diffractive imaging with a high-order harmonic source
© 2020 Optical Society of America. Users may use, reuse, and build upon the article, or use the article for text or data mining, so long as such uses are for non-commercial purposes and appropriate attribution is maintained. All other rights are reserved.Singleshot polychromatic coherent diffractive imaging is performed with a high-intensity high-order harmonic generation source. The coherence properties are analyzed and several reconstructions show the shot-to-shot fluctuations of the incident beam wavefront. The method is based on a multi-step approach. First, the spectrum is extracted from double-slit diffraction data. The spectrum is used as input to extract the monochromatic sample diffraction pattern, then phase retrieval is performed on the quasi-monochromatic data to obtain the sample’s exit surface wave. Reconstructions based on guided error reduction (ER) and alternating direction method of multipliers (ADMM) are compared. ADMM allows additional penalty terms to be included in the cost functional to promote sparsity within the reconstruction
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