ABSTRACT
This chapter considers the sparsity of a signal representation and discusses how it can be learned through dictionary learning, while its utilization in the recovery of compressed measurements is provided. It describes the cutting edge signal paradigm of low rank modeling. The chapter reports extension of state-of-the-art vector- and matrix-based approaches to high-order structured measurements using tensors and demonstrates the potential in tasks like missing measurements recovery. Measurements from multiple sensors at different locations and time instances can be encoded in a 2D sensor/time matrix. When each sensor is equipped with multiple sensing modalities, measurements are naturally encoded in a 3D sensor/modality/time structure. The chapter presents key ideas from high dimensional signal processing and analysis, involving the processing of observations ranging from single time series (1D) to multi-sensor, multi-modal observation sequences (3D). To achieve this goal, core concepts including sparsity of representation and low rank characterization are presented.
