Research And Design Of One-bit Compressive Classification

Compressive sensing(CS),which utilizes signal sparsity and nonlinear sampling to reconstruct the original signal,has been studied in many fields extensively.Although this technology can achieve dimensionality reduction of the original signal,signal reconstruction procedure suffers from high complexity.Compressive Classification(CC)only exploits compressive measurements to complete the classification in the compressive domain without reconstructing the signal.To further reduce the complexity,this thesis studies the one-bit CC based on one-bit CS.One-bit compressive classification(OBCC),which realizes classification with only the sign information of the linear projections of sources,shows practical application potentiality in scenarios where transmission bandwidth and computing resources are limited.Despite the great achievements in the aspect of CS reconstruction,research on OBCC is still in a preliminary stage.We derive and analyze the performance bounds of OBCC theoretically and design an end-to-end OBCC scheme.The main work and contributions of this thesis are as follows:Firstly,we explain the basic concepts of CS theory and classic reconstruction algorithms.We also study the basic principles of OBCC and traditional OBCC algorithms,and briefly introduces the back propagation algorithm in deep neural networks.Secondly,we propose an optimization function for OBCC,and use the distance measurement of compression classification and the characteristics of one-bit measurements to derive the theoretical expression of the upper bound of average probability of error in classification.According to the expression,the influence of the compression ratio of the measurement matrix and the statistical characteristics of the source signal on the OBCC performance is analyzed.This thesis further proposes OBCC scheme based on inner product,and the theoretical analysis results are verified by simulation experiments.At last,we put forward an end-to-end OBCC scheme based on deep neural networks(OBCC-DNN).This scheme leverages binary symmetrical channels to simulate quantization errors and channel effects,and jointly optimizes the classification network and measurement matrix to improve classification accuracy.Experimental simulations show that OBCC-DNN has better classification performance than the traditional OBCC scheme based on feature iteration.We derive the upper bound of the average probability of error in one-bit compression classification,analyze the feasibility of using single-bit classification,and design an end-to-end single-bit compression classification scheme based on deep neural networks.Experiment results show that the proposed scheme has better classification performance than traditional classification algorithms.