| Summary: | Efficient estimation and processing of high-dimensional data is important in many scientic and engineering domains. In this thesis, we explore structured sensing methods for high-dimensional signal in three different perspectives: structured random matrices for compressed sensing and corrupted sensing, atomic norm regularization for massive multiple-input-multiple-output (MIMO) systems and variable density sampling for random field. Designing efficient sensing systems for high-dimensional data by appealing to the prior knowledge that their intrinsic information is usually small has become popular in recent years. As a starting point, compressed sensing has proven to be feasible for estimating sparse signals when the number of measurements is far less than the dimensionality of the signals. Besides fully random sensing matrices, many structured sensing matrices have been designed to reduce the computation and storage cost. We propose a unified structured sensing framework and prove the associated restricted isometry property. We demonstrate that the proposed framework encompasses many existing designs. In addition, we construct new structured sensing models based on the proposed framework. Furthermore, we consider a generalized problem where the compressive measurements are affected by both dense noise and sparse corruption. We show that in some cases the proposed framework can still guarantee faithful recovery for both the sparse signal and the corruption. The next part of the thesis is concerned with channel estimation and faulty antennas detection in massive MIMO systems. By leveraging the intrinsic information of the channel matrix through atomic norm, we propose new algorithms and demonstrate their performances for both channel estimation and faulty antennas detection. In the last part, we propose a variable density sampling method for the estimation of high-dimensional random field. While conventional uniform sampling requires a number of samples increasing exponentially with the dimension, we show that faithful recovery can be guaranteed with a polynomial size of random samples.
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