Research On 1-BIT Compressed Sensing Algorithm And Its Application

In the conventional signal processing system, the process of signal sampling must abide by the Nyquist theory, i.e. the sampling rate must be at least double of the maximum frequency present in the signal. In many applications, unfortunately, it is very hard to meet this requirement because of the large bandwidth. Recently, the compressed sensing theory is proposed to ease the burden on analog-to-digital converters(ADCs) by reducing the sampling rate required to acquire and recover sparse signals stably. Practical ADCs not only sample but also quantize each measurement to a finite number of bits, the research of quantized CS is then introduced. As an extreme quantized CS, 1-Bit CS has attracted widely attention for its simple framework and perfect reconstruction performance.There have been many signal recovery algorithms in 1-bit CS theory, such as Fixed-Point Continuation(FPC), Binary Iterative Hard Thresholding(BIHT) and its derivative algorithm. Most of these algorithms required that the signal sparsity level is known, which is unpractical in practical applications. Besides, most of the existing algorithms work well only when there is no noise in the measurements, i.e. there are no sign flips, while the performance is worsened when there are a lot of sign flips in the measurements. Although the adaptive outlier pursuit(AOP) method can rduce the influence of the sign flips, with the increasing of the number of sign flips, the performance of AOP method will decay rapidly. On the other hand, the existing 1-bit CS algorithms are used to recover the one dimension signal only, the fast 1-Bit matrix CS algorithm is lack. To handle these problems, we propose some responding algorithms in this dissertation. The main contributions of this dissertation are as follows:1. To recover the original signal without the prior information of the sparsity level, two iterative reweighted methods are proposed. Firstly, the binary reweighted 1l norm minimization method gives different weights to the signal according to the order of the absolute value of each element. Secondly, the binary two-level 1l norm minimization method gives two different weights according to the order of the absolute value. Compared with the conventional 1-bit CS algorithm, the proposed methods are more applicable to practical application.2. In order to recover the signal in presence of sign flips. We treat the 1-bit CS problem as a binary classification problem and introduced a pinball loss minimization based method to recover the original signal. The proposed method utilizes the pinball loss function to replace the loss functions in existing methods. When thre are a large number of sign flips, the proposed method achieves better performance than the AOP based method.3. In order to recover an arbitrarily distributed sparse matrix from its 1-bit measurements, a matrix sketching based binary iterative hard thresholding(MSBIHT) algorithm is proposed. The MSBIHT method combine the two dimensional version of BIHT(2DBIHT) and the matrix sketching method together, then solve the sparse matrix recovery problem fastly in matrix form. To reduce the impact of the sign flips, we replace the loss function in MSBIHT method by a pinball loss function, the simulation results show the good performance.4. We extend the one dimensional BIHT method and Passive method to two dimensions case. To recover the matrix in presence of sign flips, the pinball loss function is introduced into the two dimensional BIHT, the recovery results show that the proposed method gets better performance than the two dimensional BIHT and Passive method.