基于双正交Haar域假设检验的泊松噪声快速去除
Fast Poisson Noise Removal by Biorthogonal Haar Domain Hypothesis Testing
摘要：
基于Haar域假设检验的方法被广泛用于泊松计数数据的去噪。面对大规模数据集或实时应用，Haar去噪算法必须采用抽取变换来满足有限内存或计算时间的限制。不幸的是，对于规则的底层强度，抽取产生不连续的估计和强烈的“楼梯”文物。在本文中，我们提出了HT框架与抽取双正交Haar（Bi-Haar）变换，而不是经典的Haar。Bi-Haar滤波器组被归一化，使得Bi-Haar系数（pBH）的p值对于高强度设置或大尺度提供与Haar（pH）的p值的良好近似;对于低强度设置和小尺度，我们表明pBH基本上由pH上限。因此，我们可以将基于Haar的HT应用于Bi-Haar系数以控制预定的假阳性率。通过这样做，我们受益于常规的Bi-Haar滤波器组，以获得平滑的估计，同时始终保持低的计算复杂性。建立了一个基于Fisher近似的实现HT的阈值。高光谱源通量估计的例子说明了该方法的有效性。
英文摘要：
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.
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