标题： 使用压缩测量恢复块结构激活 显示英文标题

标题： Recovering Block-structured Activations Using Compressive Measurements

摘要： 我们考虑从少量的噪声、可能自适应的压缩（线性）测量中检测和定位大型矩阵中的连续弱激活块的问题。 这与压缩感知问题密切相关，其中任务是使用少量线性测量来估计一个稀疏向量。 与压缩感知中的结果相反，其中已经证明自适应性和连续结构帮助不大，我们表明对于可靠定位，最弱信号的幅度强烈受到结构和自适应选择测量能力的影响；而对于检测，自适应性或结构都不会减少对信号幅度的要求。 我们描述了各种问题参数、信号强度以及可靠检测和定位激活块所需的测量数量之间的精确权衡。 充分条件得到了信息论下界的支持。 显示英文摘要

摘要： We consider the problems of detection and localization of a contiguous block of weak activation in a large matrix, from a small number of noisy, possibly adaptive, compressive (linear) measurements. This is closely related to the problem of compressed sensing, where the task is to estimate a sparse vector using a small number of linear measurements. Contrary to results in compressed sensing, where it has been shown that neither adaptivity nor contiguous structure help much, we show that for reliable localization the magnitude of the weakest signals is strongly influenced by both structure and the ability to choose measurements adaptively while for detection neither adaptivity nor structure reduce the requirement on the magnitude of the signal. We characterize the precise tradeoffs between the various problem parameters, the signal strength and the number of measurements required to reliably detect and localize the block of activation. The sufficient conditions are complemented with information theoretic lower bounds.