Research Of Compressive Sensing Encoding And Decoding Scheme With Low-precision Quantization

Compressive Sensing(CS)breaks through the limit of the classic Nyquist sampling theorem and implements the signal processing successfully in the way that the sampling and compression are performed simultaneously.Recently,researchers have switched the direction from reducing the sampling rate to the one of reducing the quantization accuracy,which led to the 1-bit compressed sensing theory.1-bit compressive sensing is a limited quantization scheme of classical compressive sensing measurements,which greatly relieves the hardware pressure of the encoder.Since a limited quantization is adopted and only sign information can be preserved in the sensing process,1-bit compressive sensing suffers from a much low coding efficiency.To overcome this issue,a research was made from quantizer optimization and reconstruction algorithm aspects.In this thesis,we propose a novel 1-bit vector coding and decoding scheme.Besides,we also extend the principle of 1-bit to the case of multiple bits quantization,and develop a Total Variation(TV)regularization-based reconstruction algorithm under consistent constraint whereby a better reconstruction can be achieved.The main research contents and results of the thesis are listed as follows:1.A coding and decoding scheme of compressive sensing based on 1-bit multiple description vector quantization is proposed.To overcome the low coding efficiency issue in traditional 1-bit compressive sensing,a vector quantizer is adopted to quantize partial measurements at the encoder.In addition,a Binning scheme is used to generate 1-bit code for each vector,therefore,code length is reduced.At the decoder side,by making use of the hidden correlations among the measurements,the yet-decoded measurements can be gradually estimated by those decoded ones.After decoding all measurements,an optimization algorithm is solved to obtain a high-quality reconstructed signal.Experiments show that compared with the traditional 1-bit compressive sensing quantization method,the proposed scheme can improve the coding efficiency dramatically without increasing the complexity of the encoder,and can also combat the bit loss in the channel transmission,hence possesses a robust transmission performance.2.A TV regularization based reconstruction algorithm under consistent constraint is presented.In order to reduce the redundancy existed in the 1-bit compressive sensing caused by fixed zero-value threshold quantizer,a research is conducted on the multiple-bit quantizer scheme.As distinguished from the traditional quantized compressive sensing whereby a 1-2 norm constraint is used,we introduce the idea of consistent constraint into the reconstruction process.Specifically,the quantization constraint is imposed on each measurement respectively rather than the whole measurement set,thus a better reconstruction result can be achieved.In order to cater to popular high definition image and video signals,we introduce a circular Toeplitz matrix into our compressive sensing frame,which aims to solve the computation problem in large-scale data processing.Extensive experiments show that,compared with the traditional 1-bit compressive sensing,the proposed method can raise the sampling efficiency and improve the reconstruction quality.