IEEE Trans Image Process - This is SPIRAL-TAP: Sparse Poisson Intensity Reconstruction ALgorithms--theory and practice.

Tópicos

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Resumo

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 effectively accomplished by minimizing a conventional penalized least-squares objective function. The problem addressed in this paper is the estimation of f* from y in an inverse problem setting, where the number of unknowns may potentially be larger than the number of observations and f* admits sparse approximation. The optimization formulation considered in this paper uses a penalized negative Poisson log-likelihood objective function with nonnegativity constraints (since Poisson intensities are naturally nonnegative). In particular, the proposed approach incorporates key ideas of using separable quadratic approximations to the objective function at each iteration and penalization terms related to l1 norms of coefficient vectors, total variation seminorms, and partition-based multiscale estimation methods.

Resumo Limpo

observ mani applic consist count discret event photon hit detector effect model use addit bound gaussian nois model instead requir poisson nois model result accur reconstruct spatial tempor distribut phenomenon f poisson data y effect accomplish minim convent penal leastsquar object function problem address paper estim f y invers problem set number unknown may potenti larger number observ f admit spars approxim optim formul consid paper use penal negat poisson loglikelihood object function nonneg constraint sinc poisson intens natur nonneg particular propos approach incorpor key idea use separ quadrat approxim object function iter penal term relat l norm coeffici vector total variat seminorm partitionbas multiscal estim method

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