Research On Compressive Sensing And Its Application Of Audio Codec

As an emerging theory in computational signal processing, CS has provided a novel method for data acquisition at a rate significantly below Nyquist by making signal reconstruction with a more global linear measurement scheme. The simple idea underlying it is that the sparse or compressive signals can be reconstructed from generally incomplete non-adaptive information by solving optimal problems. With trends of higher-dimensional data and larger data dynamic range , CS has shown more and more importance in the applications like medical scanners, radars and sensor networks by meeting demands in faster sampling and lower energy consumption.However, CS take fewer measurements than unknown signal values provided normally one can still recover the signal, so the linear system is typically under-determined, permitting infinitely many solutions. In this case, ways to recover signals from measurements through a computationally tractable procedure is one of the key problems of CS theory.This thesis does research on the CS theory in mathematics way as well as three kernel problems of CS----sparse representation of signal, measurement matrices and recovery algorithm. For the application of CS in the codec of audio signal, massive researches and experiments have been done on greedy algorithms such as Orthogonal Matching Pursuit (OMP), Compressive Sampling Matching Pursuit (CoSaMP), and Sparsity Adaptive Matching Pursuit (SAMP) to recover audio signals. Based on the tree structure of wavelet coefficients, a new algorithm Tree-SAMP has been proposed to recover audio signal in this thesis. Roughly speaking, the new algorithm is simpler and faster to implement than linear programming algorithms and better than simple SAMP. Besides, it achieves the effect of CoSaMP for audio signal.