Research On Compressed Sensing Image And Video Reconstruction Method

Compressed sensing(CS)is a new signal sampling paradigm presented in recent few years.Compressed sensing proposes if the signals are sparse or compressible,they can be acquired under Nyquist rate by a non-adaptive linear projection.The signal sampling paradigm based on the CS theory not only breaks through the signal sampling rate limit,but changes the traditional signal acquisition mode of first sampling and then compression.This signal sampling mode integrates data compression into the signal sampling process,thus,sensors and memories needed by signal acquisition and storing are reduced significantly.Since it provides a new technical solution for applications of efficiently and low power consuming signals sampling,CS has drawn many attentions.In past few years,along with the gradually improvement of CS theory,it has been applied in image and video compression and acquisition,synthetic aperture radar imaging,medical image processing,pattern recognition and other many fields successfully.CS theory mainly refers to three key issues including sparse representation for signals,incoherent sensing and nonlinear signal reconstruction.Nonlinear signal reconstruction is the means for signal recovery,which is also the key of the reconstructed signal quality.This dissertation firstly gives an overview of the basic theory of compressed sensing and introduces the current research status of compressed sensing theory and its application,and then focuses on the research of compressed sensing image and video reconstruction method.Main works and innovations of this dissertation include:(1)By exploiting the local correlation between pixels in spatial domain,this dissertation presents a block prediction-based compressed sensing image reconstruction method which combines the intra prediction applied in the traditional hybrid coding method into compressed sensing.Since the texture characteristics of the objects and the background in natural images are general global,the textures in a local area of the image usually exist same or similar directions and features.That is,adjacent pixels in the image have a strong correlation with each other.The proposed method is based on block-based compressed sensing framework,an image is divided into non-overlapping blocks and each image block is measured independently.The odd blocks and the even blocks are reconstructed alternately in a chessboard order.In the process of reconstruction,the image blocks are firstly predicted by pixels of the adjacent reconstructed blocks.And then the predicted residuals are reconstructed by a CS nonlinear optimizer.A few direction prediction modes are applied in the proposed method to improve the accuracy of the prediction and the reconstruction performance.The mean square error(MSE)in the measurement domain of every prediction modes are estimated and the prediction mode with the less measurement MSE is selected to conduct CS residual reconstruction.The simulation experimental results show that the proposed method combined with the intra prediction is superior to the traditional CS recovery method in the reconstruction performance for the spatial redundancies in the image are eliminated and the sparsity of the signal representation is improved.(2)Considering the temporal correlation in the video sequence,the dissertation proposes a multi-reference motion estimation and motion compensation(ME/MC)-based residual domain dictionary learning method.The statistical learning-based sparse representation dictionary is usually more robust and adaptive than the fixed sparse bases.Since the residuals between the current image frame and the adjacent image in the video sequence are sparser than the image itself,the dictionary learning from the residual domain is very likely to have stronger representation capability than those learning from the original image domain.The proposed method extracts inter-frame differences block by block from multi previous reconstructed neighbor frames as training samples by ME/MC to learn a residual domain representation dictionary.This dictionary then is employed to reconstruct the current MC frame acquired by ME.To improve the recovery performance further,a differentiated sampling mode is applied.That is,the video sequence is divided into some group of pictures(GOP)and the first frames of each GOP are defined as the key frames.The key frames are sampled in a higher sampling rate while other non-key frames are in a lower sampling rate.In the process of ME,the key frames sampled in higher sampling rate are treated as the most important reference to obtain the MC frame performing CS reconstruction.Experiments on various video sequences and sampling rates exhibit that this differentiated sampling mode improve the recovery performance considerably.(3)The dissertation proposes applying Karhunen-Loeve transform(KLT)to generate the adaptive representation dictionary in the proposed MC/ME-based dictionary learning method mentioned above to perform CS image reconstruction.The KLT which is based on the statistical characteristics of signals is the best transformation in the sense of minimum mean square error(MMSE)with a good decorrelation capability.However,KLT needs to know the signal in advance.So,it cannot be employed in the signal reconstruction applications directly.A feasible method is to construct an approximate K-L transform matrix from the signals similar to the original signals representing the original signals.There is a strong correlation between adjacent image frames in the continuous changing video sequence.The K-L transform matrixes of the similar image bocks are close to each other.The approximate K-L transform matrix learning from adjacent image frames also has a strong representation ability for the current image block.In the proposed method,the approximate K-L transform matrix is learned from the similar blocks in the training set to represent the residual of the current reconstructing block and perform the CS residual reconstruction.Compared to the optimization method based dictionary learning method,the proposed approximate KLT dictionary construction method has lower complexity and is more suitable for online learning.Compared to the traditional fixed orthogonal transform base,the proposed dictionary is based on the statistics characteristics of the signal,thus,it has a better adaptive and representation ability making the representation coefficients sparser.The experimental results demonstrate that the adaptive approximate KLT matrix based CS video reconstruction method not only achieves better performance than the discrete cosine transform(DCT)based representation method,but also is more robust against the noise than the traditional method.(4)In this dissertation,a CS image reconstruction algorithm based on the low rank optimization of the similar image block matrix is proposed to exploit the nonlocal self-similarity of the image.The general CS signal reconstruction algorithm just considers the sparsity of the signal,not taking other typical structural features in the special signal into account.The proposed method firstly utilizes a general CS reconstruction method to obtain an initial reconstruction of the image.And then,the initial image is divided into overlapping block samples and the neighbor similar blocks are grouped as similar matrixes for all block samples.The weighted nuclear norm minimization(WNNM)are employed for low rank optimization in the CS reconstruction for all grouped similar image block matrixes.The ultimate reconstruction image is weighted averaged by all reconstructed blocks.Because of the structural similarity of the image block,the grouped image block similarity matrixes are typical low rank.In some sense,the low rank of a matrix is a kind of the group sparsity of the signal.So,the proposed CS reconstruction method based on the low rank optimization of similar blocks can exploit the non-local self-similarity in the natural image and improve the reconstructed image quality.The experimental results on natural images illustrate that the proposed algorithm exceed the traditional general compressed sensing image reconstruction algorithm significantly.At last,the future work is prospected from two aspects:the low rank optimization for compressed sensing video reconstruction and the temporal multiplexing compressed sensing.