Nowadays, with the increasing demand of higher resolution and increasing number of modalities, the traditional signal/image processing hardware and software are facing significant challenges, since the Nyquist rate, which is part of the dogma for signal acquisition and processing, may become too high in many applications. How to acquire, store, fuse and process these data efficiently becomes a critical problem. The most popular solution to this problem is to compress after sensing densely. However, this over-sampling and then discarding procedure leads to a waste of energy and recourses.

A new paradigm of signal acquisition and processing, named compressive sensing (CS), was developed around 2004. Starting with the publication of “Compressed sensing” by D. Donoho, and several important publications by E. J. Candès, J. Romberg, and T. Tao, the CS theory, which links data acquisition, compression, dimensionality reduction, and optimization, has attracted much research attention.

The CS theory consists of three key components, namely, signal sparsity, incoherent measurement matrix, and signal recovery. It claims that, as long as the signal to be measured is sparse or can become sparse after some known transformation, the information in the signal can be preserved in a small number of incoherent measurements, and convex optimization offers overwhelming signal recovery probability.

The bulk of the dissertation explores the CS framework and proposes several implementations in wireless networks. Specifically, we first propose to apply compressive sensing for collaborative spectrum sensing in cognitive radio networks to reduce the amount of sensing and transmission overhead. This is realized by innovatively equipping each cognitive radio node with an on-board frequency-selective filter set, through which the sensing information was blended incoherently and can be decoded at the fusion center via joint sparsity recovery or the matrix completion technique. Then, we design a high resolution OFDM channel estimation with low-speed ADC using compressive sensing system. Aiming at increasing the channel estimation resolution without increasing the costly ADC speed, we form a random-convolution sensing scheme by carefully arranging the pilot tones and taking advantage of the channel-signal convolution nature. Moreover, based on the observation that the received signals are sparse in the time domain due to the limited multi-path effects at 60 GHz UWB wireless transmission, we designed a CS-based low-speed ADC to reduce the sampling rate, while still being able to reconstruct the signal with high fidelity. Finally, we implement the CS framework for sparse events detection in wireless sensor networks, in which the sensor activation events are sparse. We propose the use of a small number of monitoring tubes to take a very limited number of incoherent measurements, which are then decoded through the Bayesian framework with a heuristic algorithm to enhance the detection probability.