28 research outputs found
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
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
Microscopy with ultraviolet surface excitation for rapid slide-free histology.
Histologic examination of tissues is central to the diagnosis and management of neoplasms and many other diseases, and is a foundational technique for preclinical and basic research. However, commonly used bright-field microscopy requires prior preparation of micrometre-thick tissue sections mounted on glass slides, a process that can require hours or days, that contributes to cost, and that delays access to critical information. Here, we introduce a simple, non-destructive slide-free technique that within minutes provides high-resolution diagnostic histological images resembling those obtained from conventional haematoxylin-and-eosin-histology. The approach, which we named microscopy with ultraviolet surface excitation (MUSE), can also generate shape and colour-contrast information. MUSE relies on ~280-nm ultraviolet light to restrict the excitation of conventional fluorescent stains to tissue surfaces, and it has no significant effects on downstream molecular assays (including fluorescence in situ hybridization and RNA-seq). MUSE promises to improve the speed and efficiency of patient care in both state-of-the-art and low-resource settings, and to provide opportunities for rapid histology in research
POISSON IMAGE RECONSTRUCTION WITH TOTAL VARIATION REGULARIZATION
This paper describes an optimization framework for reconstructing nonnegative image intensities from linear projections contaminated with Poisson noise. Such Poisson inverse problems arise in a variety of applications, ranging from medical imaging to astronomy. A total variation regularization term is used to counter the ill-posedness of the inverse problem and results in reconstructions that are piecewise smooth. The proposed algorithm sequentially approximates the objective function with a regularized quadratic surrogate which can easily be minimized. Unlike alternative methods, this approach ensures that the natural nonnegativity constraints are satisfied without placing prohibitive restrictions on the nature of the linear projections to ensure computational tractability. The resulting algorithm is computationally efficient and outperforms similar methods using wavelet-sparsity or partition-based regularization. Index Terms — Photon-limited imaging, Poisson noise, total variation, convex optimization, sparse approximatio
SPARSITY-REGULARIZED PHOTON-LIMITED IMAGING
In many medical imaging applications (e.g., SPECT, PET), the data are a count of the number of photons incident on a detector array. When the number of photons is small, the measurement process is best modeled with a Poisson distribution. The problem addressed in this paper is the estimation of an underlying intensity from photon-limited projections where the intensity admits a sparse or low-complexity representation. This approach is based on recent inroads in sparse reconstruction methods inspired by compressed sensing. However, unlike most recent advances in this area, the optimization formulation we explore uses a penalized negative Poisson loglikelihood objective function with nonnegativity constraints (since Poisson intensities are naturally nonnegative). This paper describes computational methods for solving the nonnegatively constrained sparse Poisson inverse problem. In particular, the proposed approach incorporates sequential separable quadratic approximations to the log-likelihood and computationally efficient partition-based multiscale estimation methods
Spiral out of convexity: Sparsityregularized algorithms for photon-limited imaging
ABSTRACT The observations in many applications consist of counts of discrete events, such as photons hitting a detector, 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 2 -1 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 representation. 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