Conventional imaging modalities detect light indirectly by observing high energy photons. The random nature of photon emission and detection are often the dominant source of noise in imaging. Such case is referred to as photon-limited imaging, and the noise distribution is well modeled as Poisson. Our imaging techniques are aimed at <1Lux imaging.

## Multiplicative Multiscale Innovation (MMI)

MMI models the random partitioning of the parent Haar frame coefficient into the two child Haar frame coefficients. The partitioning follows the binomial distribution, where the denoised image can be recovered from the estimated “success/failure parameter” of the binomial distribution. Compared to the wavelet coefficients that model the magnitudes of singularities, MMI effectively models the “contrast,” or the relative magnitude of singularity between the neighboring child frame coefficients as a percentage of the parent frame coefficient magnitude. We proposed a nonparametric empirical Bayes estimator that minimize the mean square error of image contrast recovery. [Reference Code]

Nonparametric Empirical Bayes Estimation For Multiplicative Multiscale Innovation In Photon-Limited Imaging Inproceedings In: Image Processing, 2015. ICIP 2015. IEEE International Conference on, IEEE 2015. |

## Skellam Mean Estimation

Skellam distribution arises from the fact that Haar wavelet and filterbank transform coefficients corresponding to measurements of this type are distributed as sums and differences of Poisson counts. Hence Poisson image denoising problem in the pixel domain is equivalent to the *Skellam mean estimation* in the Haar wavelet domain. We were the first to report the unbiased estimate of risk (Hirakawa 2009)—application of which is best known as PURELET (Luisier 2009). We have solved for the minimum risk shrinkage operator (MRSO, Cheng 2015)—a minimizer of this risk functional that is guaranteed to outperform any other wavelet-based denoising methods. [Reference Code]

Minimum Risk Wavelet Shrinkage Operator For Poisson Image Denoising Journal Article In: IEEE Transactions on Image Processing, 2015. |

Skellam shrinkage: Wavelet-based intensity estimation for inhomogeneous Poisson data Journal Article In: Information Theory, IEEE Transactions on, (99), pp. 1–1, 2009. |

Efficient multivariate Skellam shrinkage for denoising photon-limited image data: An Empirical Bayes approach Inproceedings In: Image Processing (ICIP), 2009 16th IEEE International Conference on, pp. 2961 -2964, 2009. |

SkellamShrink: Poisson intensity estimation for vector-valued data Inproceedings In: Acoustics, Speech and Signal Processing, 2009. ICASSP 2009. IEEE International Conference on, pp. 3441 -3444, 2009. |

Wavelet-based Poisson rate estimation using the Skellam distribution Inproceedings In: Proc. SPIE, Electronic Imaging, 2009. |

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