| In recent years,with the rapid development of modern information processing technologies such as big data and artificial intelligence,methods of signal reconstruc-tion such as compressed sensing and one bit compressed sensing have been widely developed and applied.Compression sensing uses measurements that are signif-icantly less than the classical Nyquist sampling rate to recover high-dimensional sparse signals.In practical applications,in order to facilitate storage and trans-mission,sampling data usually needs to be quantized.Therefore,the research of signal reconstruction combined with the background of quantization is particularly important.As an extreme quantization case,one bit compressed sensing theory is based on a compressed sensing model,retaining only the symbol information of the measured value,and accurately reconstructing the signal by increasing the number of measurements.How to reconstruct signals with fewer measurements has also become a huge challenge in research.In many practical applications,signals not only exhibit sparsity,but also ex-hibit other special structures,such as block sparsity,dictionary sparsity,and partial element information of known signals.Based on the theory of one bit compressed sensing,this work studies the reconstruction of partitioned sparse signals,including the reconstruction of the direction and magnitude of the signal,as well as the pro-pose of the algorithm and simulations.To some extent,this paper generalizes the results of the one bit compressed sensing method in signal reconstruction,optimizes the conditions for signal recovery,and reduces the required number of measurements signal recovery.The main contents are as follows:The first chapter introduces the research background,significance,research status and applications of one bit compression sensing in detail.The second chapter gives a unified explanation of the commonly used mathe-matical symbols in this work.Then,we introduce some definitions and theorems about-net,covering number and packing number.At last,we introduce the concept of block sparse signals,block partitioning methods,and related definitions.The third chapter introduces the reconstruction of the direction based on stan-dard one bit measurement in detail.Propose the definition ofl2/leffective block-sparsity,establish the model and give the theoretical proof.The results show that by solving the proposedl2/l-minimization model can obtain the estimated value of the direction of the signal to be recovered,the lower bound of the mea-surement number,and the error bound with a high probability,and ensure that the required lower bound of the measurement number is not higher than other existing one bit compression sensing recovery methods for sparse signals,and improving the reconstruction accuracy.The fourth chapter introduces the reconstruction of the magnitude based on threshold one bit measurement in detail.Including the establishment of the model and the proof of the main conclusions.The results show that by solving the proposed model,the magnitude of the signal to be recovered and the lower bound of the measurement number can be obtained with high probability,and the lower bound of the measurement number required to achieve the reconstruction accuracy can be guaranteed to be no higher than other existing one bit compressed sensing recovery methods.In the fifth chapter,we first design a block adaptive binary iterative threshold（BABIT）algorithm.Next,we show the convergence of the algorithm.Simulat-ed numerical experiments and real data experiments are conducted to verify the effectiveness of the algorithm.By comparing the proposed block adaptive binary iterative threshold algorithm with other algorithms,the superiority of the algorithm in recovery performance is verified.The last chapter summarizes the work of this paper,and it has a corresponding outlook. |
