Signal Reconstruction Based On High Order Expansion FMM And Low Rank Matrix Recovery

With the rise and development of Internet, the data(signals) of people received grow exponentially. However, for various reasons, the signals will also appear to lack. This thesis mainly studied on reconstruction of the missing signals using high order expansion fast marching method(FMM) and low rank matrix recovery(LRMR) algorithm and showed the application of the algorithms in three aspects: seismic data reconstruction; digital image restoration; video background modeling.(1) Seismic signals reconstruction algorithm based on high order expansion fast marching method.The algorithm uses local reconstruction mode. Firstly, the missing seismic data is mapped into seismic images and followed by the analysis of quantization error in the mapping. After that, the seismic image is decomposed using wavelet transform with two down-sampling. The low-frequency part of the decomposition uses high order expansion FMM for local by-point reconstruction. The high-frequency part is reconstructed by the horizontal, vertical and diagonal prediction filtering of the reconstituted low-frequency part. Then, the reconstructed seismic image is obtained by the inverse wavelet transform. Finally, the obtained seismic image is mapped into the seismic signals. Pre-stack and post-stack seismic signals reconstruction experiments verify the feasibility of algorithms. The comparison with traditional algorithms based on morphological component analysis(MCA), and the K-SVD dictionary learning, has shown that the proposed algorithm has faster reconstruction speed and higher reconstruction precision.(2) Traditional low rank matrix recovery algorithm can not restore missing dead lines or thin strips in the digital images. This thesis proposes an image restoration algorithm by combining LRMR with high order expansion FMM.Considering high order expansion FMM based on the physical thermal diffusion principle, can restore the missing dead lines or thin strips of image effectively. Firstly we detect the location of dead lines or thin strips. After that we restore them by the high order expansion FMM. Finally the image is restored by LRMR in which the optimization problem is solved with precise augmented Lagrange multiplier(ALM) algorithm. The experimental results verify the feasibility and efficiency of the proposed algorithm. Compared with traditional LRMR algorithm, it has higher restoration precision.(3) Traditional low rank matrix recovery(LRMR) algorithm cannot remove the larger foreground of video through dividing video into frames. This paper presents a video background modeling algorithm of combining LRMR with high order expansion fast marching method(FMM).Due to the high order expansion FMM can also restore the larger missing region, making up for the smaller missing region of LRMR in the video background modeling effectively. Firstly, remove the smaller sparse noise of the prospects in each frame using LRMR algorithm; then through the inter frame difference method determines the larger regional prospects position in video frame; and then restore the occluded regions by larger prospects through high order expansion FMM, modeling background frame by frame. The simulation experiments of indoor and outdoor videos show that the proposed algorithm is better than LRMR background modeling algorithm frame by frame, and the inter-frame difference method.