Real-word signals are often sparse in that they have compact representation by using proper bases. Notable examples are digital images which can be compactly represented and compressed via various compression techniques. Sparsity exploitation has proven a powerful tool for the acquisition, transmission, and storage of high-dimensional signals. Remarkably, it allows recovering the entire signal from relatively few measurements. Many sparse signals such as images, audio and video signals also exhibit some sparsity pattern (e.g., clustered or block sparse coefficients) that admits more efficient signal recovery. However, when the sparsity pattern is irregular or unknown, how to efficiently recover the signal from a few measurements is still largely an uncharted territory. This is the first research thrust pursued in this project. Meanwhile, for signal acquisition, practical systems usually employ quantization which converts each measurement into a few binary bits to facilitate processing and storage. The effect of quantization, however, was neglected by most classical sparse signal recovery methods. Only recently, sparse signal reconstruction/estimation which explicitly accounts for the effect of quantization started to receive attention, although most such works just considered heuristic quantizers. A second research thrust of this project examines two problems related to quantization: (1) development of efficient signal recovery algorithms with quantized measurements; and (2) optimum quantizer design for sparse signal recovery, in particular for the case of low-rate quantization which is required in many sensing systems that have bandwidth/power constraints. This project also has a significant educational component aimed to provide integrated research experience and training for undergraduate and graduate students.
This project takes several approaches to address the above problems. First, on clustered sparse signal recovery, the PI proposes a new Bayesian learning framework for sparse signal recovery with unknown block sparsity structure. The proposed research builds on a novel Bayesian hierarchical model involving coupled hyperparameters to promote block sparsity without imposing rigid block structures. Based on the proposed models, a range of Bayesian inference algorithms are to be developed, taking into account of computational efficiency and robustness to noise. Second, on low-rate quantizer design, the PI proposes an adaptive quantization approach to enhance the reconstruction performance of sparse signal recovery algorithms taking quantized measurements. The proposed approach involves sequentially quantizing each measurement, using past quantized bits to predict the next sample to be quantized, and finally thresholding at the predicted value. Third, on the development of reconstruction algorithms using quantized measurements, the PI proposes to employ a sigmoid function to impose a consistency constraint between the reconstructed signal and the quantized measurements, which is shown to offer the benefit of computational complexity reduction and significant reconstruction accuracy improvement over existing methods.
