This is SPIRAL-TAP: Sparse Poisson Intensity Reconstruction ALgorithms—Theory and Practice

By Zachary T. Harmany, Roummel F. Marcia, Rebecca M. Willett. IEEE Transactions on Image Processing, 2010

312 citations recorded by the source corpus.

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.

Subfields: Environmental Engineering, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/18b04752a09119494d21c9d57c6097e9595be8c8

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Citations in the corpus

Plug-and-Play ADMM for Image Restoration: Fixed-Point Convergence and Applications (2016, methodology): “We are aware of other existing Poisson denoising methods such as [17], [37], [49]–[51].”
Poisson Noise Reduction with Non-local PCA (2012, methodology): “The algorithm proposed in [29] can be adapted with the SpaRSA step provided in [44], or in our setting by using its adaptation to the Poisson case—SPIRAL [20].”
Computational segmentation of collagen fibers from second-harmonic generation images of breast cancer (2014, methodology): “SPTV was shown to perform well at highlighting strong edges in images and smooth noise in low-gradient areas.(24) The designers of this algorithm have tested it on noisy computed tomography reconstruction data; however, it has not been heretofore applied to preprocessing for fiber extraction from SH”