Fast Poisson Noise Removal by Biorthogonal Haar Domain Hypothesis Testing

Methods based on hypothesis tests (HTs) in the Haar domain are widely used to denoise Poisson count data. However, facing large datasets or real-time applications, Haar-based denoisers have to use the decimated transform to meet limited-memory or computation-time constraints. Unfortunately, for regular underlying intensities, decimation yields discontinuous estimates and strong “staircase” artifacts. In this paper, we propose to combine the HT framework with the decimated biorthogonal Haar (Bi-Haar) transform instead of classical Haar. It is shown that the Bi-Haar coefficients converge asymptotically to Haar coefficients in distribution as the transform scale increases. The convergence rate also increases with the data dimension. Thus, we are allowed to directly apply the Haar-based HTs to Bi-Haar coefficients, especially when processing high-dimensional large datasets. By doing so, we benefit from the regular Bi-Haar filter bank to gain a smooth estimate while always maintaining a low computational complexity. The efficiency of this method is also illustrated on an example of hyperspectral-source-flux estimation.