标题： 信号恢复在子空间并集中的应用与压缩成像 显示英文标题

标题： Signal Recovery in Unions of Subspaces with Applications to Compressive Imaging

摘要： 在从通信到遗传学的各种应用中，信号可以建模为位于子空间的并集中。 在该模型下，位于某些子空间中的信号系数会同时激活或不激活。 潜在的子空间是预先已知的，但具体的活跃子空间集合（即信号支持）必须从测量中学习。 我们表明，利用子空间的知识可以进一步减少精确信号恢复所需的测量数量，并推导出所需测量数的通用界限。 该界限具有普遍性，因为它仅取决于所考虑的子空间数量及其相互之间的方向。 子空间的具体细节（例如，组成、维度、范围、重叠等）不影响我们得到的结果。 在此过程中，我们推导了重叠组的组套索（latent group lasso）特殊情况的样本复杂度界限，该方法被用于各种应用中。 最后，我们还表明，图像的小波变换系数可以建模为位于组中，因此可以使用组套索方法高效恢复。 显示英文摘要

摘要： In applications ranging from communications to genetics, signals can be modeled as lying in a union of subspaces. Under this model, signal coefficients that lie in certain subspaces are active or inactive together. The potential subspaces are known in advance, but the particular set of subspaces that are active (i.e., in the signal support) must be learned from measurements. We show that exploiting knowledge of subspaces can further reduce the number of measurements required for exact signal recovery, and derive universal bounds for the number of measurements needed. The bound is universal in the sense that it only depends on the number of subspaces under consideration, and their orientation relative to each other. The particulars of the subspaces (e.g., compositions, dimensions, extents, overlaps, etc.) does not affect the results we obtain. In the process, we derive sample complexity bounds for the special case of the group lasso with overlapping groups (the latent group lasso), which is used in a variety of applications. Finally, we also show that wavelet transform coefficients of images can be modeled as lying in groups, and hence can be efficiently recovered using group lasso methods.