Memory-Limited stochastic approximation for poisson subspace tracking

Poisson noise is ubiquitously encountered in applications including medical and photon-limited imaging. We consider the problem of recovering and tracking the underlying Poisson rate, where the rate vector is assumed to lie in an unknown low-dimensional subspace, with possibly missing entries. A stochastic approximation (SA) algorithm is proposed to solve the problem. This algorithm alternates between two steps. It sequentially identifies the underlying subspace, and recovers coefficients associated with the subspace. The SA algorithm is then modified to obtain a memory-efficient algorithm without storing all historic data. Two theoretical performance guarantees are establish regarding the convergence of SA algorithm. Numerical experiments are provided to demonstrate the proposed algorithms for Poisson video. The memory-limited SA algorithm is shown to empirically yield similar performances to the original SA algorithm.

在包括医疗和光子受限成像在内的应用中，泊松噪声无处不在。我们考虑恢复和跟踪基础泊松率的问题，该泊松率假定速率向量位于未知的低维子空间中，可能缺少条目。提出了随机近似（SA）算法来解决该问题。该算法在两个步骤之间交替。它依次识别基础子空间，并恢复与子空间相关的系数。然后对SA算法进行修改，以获得记忆效率的算法，而无需存储所有历史数据。关于SA算法的融合，建立了两个理论性能保证。提供了数值实验，以证明泊松视频的提议算法。记忆限制的SA算法显示出与原始SA算法相似的性能。