Key to successfully deal with complex contemporary datasets is the development of tractable models that account for the irregular structure of the information at hand. This paper provides a comprehensive and unifying view of several sampling, reconstruction, and recovery problems for signals defined on irregular domains that can be accurately represented by a graph. The workhorse assumption is that the (partially) observed signals can be modeled as the output of a graph filter to a structured (parsimonious) input graph signal. When either the input or the filter coefficients are known, this is tantamount to assuming that the signals of interest live on a subspace defined by the supporting graph. When neither is known, the model becomes bilinear. Upon imposing different priors and additional structure on either the input or the filter coefficients, a broad range of relevant problem formulations arise. The goal is then to leverage those priors, the shift operator of the supporting graph, and the samples of the signal of interest to recover: the signal at the non-sampled nodes (graph-signal interpolation), the input (deconvolution), the filter coefficients (system identification), or any combination thereof (blind deconvolution).

成功处理复杂的当代数据集的关键是开发可解释手头信息不规则结构的易处理模型。本文对定义在不规则域上的信号的几个采样、重建和恢复问题提供了一个全面而统一的观点，这些问题可以用图形准确表示。主力假设是（部分）观察到的信号可以建模为图形滤波器的输出到结构化（简约）输入图信号。当输入或滤波器系数已知时，这相当于假设感兴趣的信号存在于由支持图定义的子空间中。当两者都不知道时，模型变为双线性。在对输入或滤波器系数施加不同的先验和附加结构后，会出现广泛的相关问题公式。然后目标是利用这些先验、支持图的移位算子和感兴趣的信号样本来恢复：非采样节点处的信号（图信号插值）、输入（反卷积）、滤波器系数（系统识别）或其任意组合（盲解卷积）。