  Methods based on hypothesis tests (HTs) in the Haar domain are widely used to
denoise Poisson count data. 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 the classical Haar.
The Bi-Haar filter bank is normalized such that the p-values of Bi-Haar
coefficients (pBH) provide good approximation to those of Haar (pH) for
high-intensity settings or large scales; for low-intensity settings and small
scales, we show that pBH are essentially upper-bounded by pH. Thus, we may
apply the Haar-based HTs to Bi-Haar coefficients to control a prefixed false
positive rate. By doing so, we benefit from the regular Bi-Haar filter bank to
gain a smooth estimate while always maintaining a low computational complexity.
A Fisher-approximation-based threshold imple- menting the HTs is also
established. The efficiency of this method is illustrated on an example of
hyperspectral-source-flux estimation.
