560 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
Bits from Photons: Oversampled Image Acquisition Using Binary Poisson Statistics
We study a new image sensor that is reminiscent of traditional photographic
film. Each pixel in the sensor has a binary response, giving only a one-bit
quantized measurement of the local light intensity. To analyze its performance,
we formulate the oversampled binary sensing scheme as a parameter estimation
problem based on quantized Poisson statistics. We show that, with a
single-photon quantization threshold and large oversampling factors, the
Cram\'er-Rao lower bound (CRLB) of the estimation variance approaches that of
an ideal unquantized sensor, that is, as if there were no quantization in the
sensor measurements. Furthermore, the CRLB is shown to be asymptotically
achievable by the maximum likelihood estimator (MLE). By showing that the
log-likelihood function of our problem is concave, we guarantee the global
optimality of iterative algorithms in finding the MLE. Numerical results on
both synthetic data and images taken by a prototype sensor verify our
theoretical analysis and demonstrate the effectiveness of our image
reconstruction algorithm. They also suggest the potential application of the
oversampled binary sensing scheme in high dynamic range photography
3D Raman mapping of the collagen fibril orientation in human osteonal lamellae
AbstractChemical composition and fibrillar organization are the major determinants of osteonal bone mechanics. However, prominent methodologies commonly applied to investigate mechanical properties of bone on the micro scale are usually not able to concurrently describe both factors. In this study, we used polarized Raman spectroscopy (PRS) to simultaneously analyze structural and chemical information of collagen fibrils in human osteonal bone in a single experiment. Specifically, the three-dimensional arrangement of collagen fibrils in osteonal lamellae was assessed. By analyzing the anisotropic intensity of the amide I Raman band of collagen as a function of the orientation of the incident laser polarization, different parameters related to the orientation of the collagen fibrils and the degree of alignment of the fibrils were derived. Based on the analysis of several osteons, two major fibrillar organization patterns were identified, one with a monotonic and another with a periodically changing twist direction. These results confirm earlier reported twisted and oscillating plywood arrangements, respectively. Furthermore, indicators of the degree of alignment suggested the presence of disordered collagen within the lamellar organization of the osteon. The results show the versatility of the analytical PRS approach and demonstrate its capability in providing not only compositional, but also 3D structural information in a complex hierarchically structured biological material. The concurrent assessment of chemical and structural features may contribute to a comprehensive characterization of the microstructure of bone and other collagen-based tissues
Restoration of Poissonian Images Using Alternating Direction Optimization
Much research has been devoted to the problem of restoring Poissonian images,
namely for medical and astronomical applications. However, the restoration of
these images using state-of-the-art regularizers (such as those based on
multiscale representations or total variation) is still an active research
area, since the associated optimization problems are quite challenging. In this
paper, we propose an approach to deconvolving Poissonian images, which is based
on an alternating direction optimization method. The standard regularization
(or maximum a posteriori) restoration criterion, which combines the Poisson
log-likelihood with a (non-smooth) convex regularizer (log-prior), leads to
hard optimization problems: the log-likelihood is non-quadratic and
non-separable, the regularizer is non-smooth, and there is a non-negativity
constraint. Using standard convex analysis tools, we present sufficient
conditions for existence and uniqueness of solutions of these optimization
problems, for several types of regularizers: total-variation, frame-based
analysis, and frame-based synthesis. We attack these problems with an instance
of the alternating direction method of multipliers (ADMM), which belongs to the
family of augmented Lagrangian algorithms. We study sufficient conditions for
convergence and show that these are satisfied, either under total-variation or
frame-based (analysis and synthesis) regularization. The resulting algorithms
are shown to outperform alternative state-of-the-art methods, both in terms of
speed and restoration accuracy.Comment: 12 pages, 12 figures, 2 tables. Submitted to the IEEE Transactions on
Image Processin
Coronal Mass Ejection Detection using Wavelets, Curvelets and Ridgelets: Applications for Space Weather Monitoring
Coronal mass ejections (CMEs) are large-scale eruptions of plasma and
magnetic feld that can produce adverse space weather at Earth and other
locations in the Heliosphere. Due to the intrinsic multiscale nature of
features in coronagraph images, wavelet and multiscale image processing
techniques are well suited to enhancing the visibility of CMEs and supressing
noise. However, wavelets are better suited to identifying point-like features,
such as noise or background stars, than to enhancing the visibility of the
curved form of a typical CME front. Higher order multiscale techniques, such as
ridgelets and curvelets, were therefore explored to characterise the morphology
(width, curvature) and kinematics (position, velocity, acceleration) of CMEs.
Curvelets in particular were found to be well suited to characterising CME
properties in a self-consistent manner. Curvelets are thus likely to be of
benefit to autonomous monitoring of CME properties for space weather
applications.Comment: Accepted for publication in Advances in Space Research (3 April 2010
Sparse Poisson Intensity Reconstruction Algorithms
The observations in many applications consist of counts of discrete events,
such as photons hitting a dector, which cannot be effectively modeled using an
additive bounded or Gaussian noise model, and instead require a Poisson noise
model. As a result, accurate reconstruction of a spatially or temporally
distributed phenomenon (f) from Poisson data (y) cannot be accomplished by
minimizing a conventional l2-l1 objective function. The problem addressed in
this paper is the estimation of f from y in an inverse problem setting, where
(a) the number of unknowns may potentially be larger than the number of
observations and (b) f admits a sparse approximation in some basis. The
optimization formulation considered in this paper uses a negative Poisson
log-likelihood objective function with nonnegativity constraints (since Poisson
intensities are naturally nonnegative). This paper describes computational
methods for solving the constrained sparse Poisson inverse problem. In
particular, the proposed approach incorporates key ideas of using quadratic
separable approximations to the objective function at each iteration and
computationally efficient partition-based multiscale estimation methods.Comment: 4 pages, 4 figures, PDFLaTeX, Submitted to IEEE Workshop on
Statistical Signal Processing, 200
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