Kota Pavan K, LeJeune Daniel, Drezek Rebekah A, Baraniuk Richard G
Department of Bioengineering, Rice University, Houston, TX 77005 USA.
Department of Electrical and Computer Engineering, Rice University, Houston, TX 77005 USA.
IEEE Trans Signal Process. 2022;70:2388-2401. doi: 10.1109/tsp.2022.3172028. Epub 2022 May 3.
Compressed sensing (CS) is a signal processing technique that enables the efficient recovery of a sparse high-dimensional signal from low-dimensional measurements. In the multiple measurement vector (MMV) framework, a set of signals with the same support must be recovered from their corresponding measurements. Here, we present the first exploration of the MMV problem where signals are independently drawn from a sparse, multivariate Poisson distribution. We are primarily motivated by a suite of biosensing applications of microfluidics where analytes (such as whole cells or biomarkers) are captured in small volume partitions according to a Poisson distribution. We recover the sparse parameter vector of Poisson rates through maximum likelihood estimation with our novel Sparse Poisson Recovery (SPoRe) algorithm. SPoRe uses batch stochastic gradient ascent enabled by Monte Carlo approximations of otherwise intractable gradients. By uniquely leveraging the Poisson structure, SPoRe substantially outperforms a comprehensive set of existing and custom baseline CS algorithms. Notably, SPoRe can exhibit high performance even with one-dimensional measurements and high noise levels. This resource efficiency is not only unprecedented in the field of CS but is also particularly potent for applications in microfluidics in which the number of resolvable measurements per partition is often severely limited. We prove the identifiability property of the Poisson model under such lax conditions, analytically develop insights into system performance, and confirm these insights in simulated experiments. Our findings encourage a new approach to biosensing and are generalizable to other applications featuring spatial and temporal Poisson signals.
压缩感知（CS）是一种信号处理技术，能够从低维测量中高效恢复稀疏高维信号。在多测量向量（MMV）框架中，必须从相应测量中恢复一组具有相同支撑集的信号。在此，我们首次探索了MMV问题，其中信号独立地从稀疏多元泊松分布中抽取。我们的主要动机来自于一系列微流控生物传感应用，其中分析物（如全细胞或生物标志物）根据泊松分布被捕获在小体积分区中。我们通过使用新颖的稀疏泊松恢复（SPoRe）算法进行最大似然估计来恢复泊松率的稀疏参数向量。SPoRe使用由难以处理的梯度的蒙特卡罗近似实现的批量随机梯度上升。通过独特地利用泊松结构，SPoRe显著优于一组全面的现有和定制基线CS算法。值得注意的是，即使在一维测量和高噪声水平下，SPoRe也能表现出高性能。这种资源效率不仅在CS领域是前所未有的，而且对于微流控应用特别有效，在微流控应用中每个分区可分辨测量的数量通常受到严重限制。我们证明了在这种宽松条件下泊松模型的可识别性，通过分析深入了解系统性能，并在模拟实验中证实了这些见解。我们的发现鼓励了一种新的生物传感方法，并且可以推广到其他具有空间和时间泊松信号的应用中。
