SPIRAL out of convexity: sparsity-regularized algorithms for photon-limited imaging

Zachary T. Harmany; Roummel F. Marcia; Rebecca M. Willett

doi:10.1117/12.850771

27 January 2010 SPIRAL out of convexity: sparsity-regularized algorithms for photon-limited imaging

Zachary T. Harmany, Roummel F. Marcia, Rebecca M. Willett

Proceedings Volume 7533, Computational Imaging VIII; 75330R (2010) https://doi.org/10.1117/12.850771
Event: IS&T/SPIE Electronic Imaging, 2010, San Jose, California, United States

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 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 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.

Citation Download Citation

Zachary T. Harmany, Roummel F. Marcia, and Rebecca M. Willett "SPIRAL out of convexity: sparsity-regularized algorithms for photon-limited imaging", Proc. SPIE 7533, Computational Imaging VIII, 75330R (27 January 2010); https://doi.org/10.1117/12.850771

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