Multitask Compressive Sensing
Multitask Compressive Sensing
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DOI：
10.1109/tsp.2008.2005866
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发表时间：
2009-01-01
影响因子：
5.4
通讯作者：
Carin, Lawrence
中科院分区：
文献类型：
--
作者：
Ji, Shihao;Dunson, David;Carin, Lawrence
压缩感测（CS）是一种框架，由此执行N个非自适应测量以构成向量uppermix是R-N的元素，其中uppermix用于将cap是R-M的元素上的近似（u）恢复到期望信号u是R-M的元素，其中N（u）over cap可以以与（2）（2）具有类似于最佳自适应变换的渐近性质的误差平行于u（u）over cap来执行。编码算法应用于基T.映射upper->（u）over cap构成了一个逆问题，通常使用l（1）正则化或相关技术来解决。在大多数先前的研究中，如果执行L > 1组压缩测量{upper（i）}（i）=1，L，则每次独立地恢复相关联的{（u）over cap（i）}（i）=1，L中的每一个。在许多应用中，由cap（i）上的映射upperset（i）->（u）定义的L个“任务”在统计上不是独立的，并且如果利用统计相互关系，则可以提高反演的性能。在本文中，我们在多任务学习设置中解决这个问题，其中每个任务的映射v1-u1对应于推断与所需信号u1相关联的参数（这里是小波系数），并且共享先验分布在所有L个任务中。在这种分层贝叶斯建模下，来自所有L个任务的数据有助于推断超参数的后验，并且一旦由此推断出共享先验，则来自L个单独任务中的每个任务的数据然后被用于估计任务相关的小波系数。一个经验贝叶斯过程的超参数估计被认为是两个快速推理算法扩展的相关向量机（RVM）的开发。几个数据集上的实例结果表明，所提出的算法的有效性和鲁棒性。
Compressive sensing (CS) is a framework whereby one performs N nonadaptive measurements to constitute a vector upsilon is an element of R-N, with upsilon used to recover an approximation (u) over cap is an element of R-M to a desired signal u is an element of R-M, with N (u) over cap may be performed with error parallel to u - (u) over cap parallel to(2)(2) having asymptotic properties analogous to those of the best adaptive transform-coding algorithm applied in the basis T. The mapping upsilon -> (u) over cap constitutes an inverse problem, often solved using l(1) regularization or related techniques. In most previous research, if L > 1 sets of compressive measurements {upsilon(i)}(i)=1, L are performed, each of the associated {(u) over cap (i)}(i)=1, L are recovered one at a time, independently. In many applications the L "tasks" defined by the mappings upsilon(i) -> (u) over cap (i) are not statistically independent, and it may be possible to improve the performance of the inversion if statistical interrelationships are exploited. In this paper, we address this problem within a multitask learning setting, wherein the mapping v; - u; for each task corresponds to inferring the parameters (here, wavelet coefficients) associated with the desired signal u;, and a shared prior is placed across all of the L tasks. Under this hierarchical Bayesian modeling, data from all L tasks contribute toward inferring a posterior on the hyperparameters, and once the shared prior is thereby inferred, the data from each of the L individual tasks is then employed to estimate the task-dependent wavelet coefficients. An empirical Bayesian procedure for the estimation of hyperparameters is considered; two fast inference algorithms extending the relevance vector machine (RVM) are developed. Example results on several data sets demonstrate the effectiveness and robustness of the proposed algorithms.