Compressed Sensing Based Background Extraction And Image Fusion

Sampling technology is the bridge that to communicate the real world analog signals with advanced digital signal processing technology. Under the premise of that the sampling procedure can retain the complete information of the signal, people hope to use smaller sampling rate for better, so that makes hardware implementation easier and saves storage, transmission and computing overhead. Traditional signal processing methods usually do the sampling process first, and then compress the sampled data to save storage and transmission cost. Recent years, a new theory called compressed sensing provides a new way of signal processing. If the signal is known to have some type of sparse feature, then a small amount of linear projection of the signal can retain signal integrity information, and the reverse problem can be solved by sparse signal reconstruction algorithms. Compressed sensing achieves compression while the sampling procedure and sampling rate does not determined by the signal bandwidth, but depends on sparse characteristics of the signal. Single-pixel camera is the hardware built based on the theory of compressed sensing imaging, which uses a single photon detector to obtain the random measurements of the original scene. The imaging quality related to the number of measurements, which makes low resolution camera to obtain high-resolution images possible.Since the emergence of single-pixel camera, it is very necessary to find the signal processing method in the compressed sensing domain. This kind of signal processing is to find effective ways to deal directly in the compressed sensing domain to achieve the desired effect, avoiding multiple reconstruction process. In addition, in the field of video and image processing, background extraction/modeling and image fusion has very practical value. Therefore, the background extraction/modeling and image fusion in the compressed sensing domain is very meaningful.This study of this article is based on the image and video data that obtained by the single-pixel camera, and process background extraction and image fusion directly in the compressed sensing domain. The main work and contribution are as follows:1. Overview the framework of compressed sensing theory and the main algorithms of each components of the framework. Introduce the commonly used sparse representation methods methods of measurement matrix construction and reconstruction algorithms, and the advantages and disadvantages of each method. Analyze the working principle and structure of single-pixel camera.2. Propose a framework of compressed sensing domain background extraction processing, and presents four simple and effective algorithms for compressed sensing domain background extraction. The framework works by directly operates on the compressed sensing domain data to get the compressed sensing measurements of background image. The background image can be reconstructed by existing methods, avoiding the reconstruction of each frame, that saves storage, transmission and computing cost effectively. The algorithms used for background extraction were average, moving average, median, and the selected method. The measurements of the background image obtained by these four methods will be used as known in the operation of background subtraction based on compressed sensing, and achieved satisfactory results.3. Propose a fusion rule in compressed sensing domain. The fusion rule of maximum measurement energy is proposed in the existing image fusion framework of compressed sensing domain. Based on the important criteria of compressed sensing-the Restricted Isometry Principle (RIP), we can infer that the processing of compressed sensing can maintain the energy of signals. Natural images usually have sparse representation in the wavelet domain, so before and after the process of much. And the maximum energy of the wavelet coefficient is a commonly used fusion rules. Based on these facts, the fusion rule of maximum measurement energy is proposed.