矿井智能监测系统是保障煤矿生产的关键环节，但受制于有限的井下通信资源，在基于奈奎斯特采样定理的传输模式下，难以保证采集到的视频图像质量，而基于稀疏理论的压缩感知传输模型，其新的传输架构有效改变了这一现状。稀疏重建作为压缩感知模型的重要组成部分，对图像的成像质量起到了至关重要的作用，因此，有必要在新的传输框架下，研究重建算法的收敛性能，为后续算法提供理论支撑。同时，有必要设计出高效鲁棒的算法以保证信号的重建精度。此外，由于井下环境的特殊性、复杂性，矿井监测系统工作时，面临光照分布不均，光照强度低，以及多源噪声的影响，传统的人工监测手段存在问题较多，监测效率及准确性方面均难以满足煤矿安全生产的需求，因此，有必要进一步加快视觉技术的应用，从而在提升监测系统智能化水平的同时，通过目标检测、跟踪等措施为后续的预警联动机制提供更为有力的保障。

本文以稀疏理论为核心基础，围绕矿井监测中存在图像重建精度低，目标检测跟踪鲁棒性，稳定性差的问题。重点研究了稀疏重建算法的收敛性能、基于广度和深度优先的多路径重建算法、基于贝叶斯理论的多观测联合稀疏重建算法和基于稀疏表示的目标检测跟踪算法，并进一步延伸到跨摄像头跟踪领域。主要研究内容如下：

针对解码端存在扰动干扰以及多观测稀疏信号的RIP性能界限问题，本文以原子相干性为切入点。首先在单观测稀疏信号模型中，推导出了BLOOMP算法在完全扰动条件下重建信号的RIP性能界限。其次，将BLOOMP算法推广到多观测稀疏信号模型中，提出了带排除局部最优同步正交匹配追踪（BLO-SOMP）算法，并推导了该算法在理想状态下准确重建信号的RIP性能界限。给出了该算法在有噪条件和扰动条件下准确重建信号的充分条件和重建误差范围。

研究了单观测稀疏模型的井下图像重建问题。针对传统多路径算法重建性能低的问题，提出两种新的多路径匹配追踪算法。在提出的加速MMP算法中，通过采用阈值门限和修剪树模型策略，使正确的分解点遍历更多的有效支撑，减少冗余路径，并在理论上推导了加速MMP算法的收敛条件。在提出的路径自适应匹配追踪算法中，通过粒子群优化构造路径基底，结合重建系数，设计了择优选择逐步增加路径数的策略，并利用正则化方法对支撑集进行二次评价，提升支撑精度。在标准图像以及井下图像重建实验中，本文所提两种算法有着良好的性能表现，并很好的兼顾了重建效率。

研究了多观测联合模型的井下图像重建问题。针对复杂环境下存在噪声干扰及信号支撑位未知的问题，提出两种新的基于贝叶斯理论的重建算法。在提出的基于最大后验比的重建算法中，分别利用高斯和多元拉普拉斯分布刻画噪声源与未知信号的稀疏性，建立了基于高斯观测矩阵的相关系数分布模型。依据最大后验比并结合前向后向匹配追踪算法，设计了一种新的匹配策略，用于求解欠定方程最优解。在所提基于贝叶斯分层模型的重建算法中，首先建立具有结构化性质的分层贝叶斯模型以表征联合信号的先验信息。其次，采用多元匹配准则并联合变分法获得隐变量初始期望，并将其作为联合支撑的先验信息。然后利用所获信息，推导得到修正因子并结合回溯策略优化了欠定方程的代价函数，最后引入两段式SFBP算法，实现支撑的精确估计。重建实验中，本文所提两种算法在支撑位置未知及噪声干扰下，具有更为可靠稳定的重建性能。

针对多源噪声影响导致检测准确度不高的问题，提出一种基于稀疏表示的目标检测算法。通过非均值滤波技术滤除多源噪声，在采用改进的K-SVD字典完成背景建模的基础上，结合稀疏表示框架实现目标的准确检测。实验结果表明，本文算法保证了稳定检测准确性，并且能更好的适应井下特殊环境。在目标跟踪阶段，针对光照，噪声等外界干扰导致的跟踪准确率不高的问题，提出一种基于稀疏表示的运动目标跟踪模型。首先，对视频图像进行光照归一化处理，通过小波变换获取不同频率信息的子带，对低频部分采用直方图均衡技术改善光照，并结合加权引导滤波对高频部分进行降噪处理；再运用时频逆小波变换获取优化后的目标图像。其次，在目标重建阶段，引入新的判别条件更新相关集半径以获得更为精确的支撑集，从而减少重建误差。最后，在字典更新阶段，设计了新的监督机制，利用相关集分别对目标与判别模板的相似度进行排序，并选定符合条件的原子进行替换，以减少误差累积。井上及井下跟踪实验表明，本文所提算法在准确性，鲁棒性方面均有较好的表现。

针对跨摄像头下由于不同摄像头所涵盖区域存在差异性以及运动目标行为轨迹具有随机性，导致误差积累，影响跟踪准确度的问题，提出一种结合稀疏表示理论的跟踪模型。该模型首先通过不同摄像头间的背景亮度值，给出了亮度补偿公式，建立补偿模板。其次，引入BLOOMP算法，通过局部优化技术与新的相干性判别机制结合，获得更为紧凑的相关带，以优化跟踪模型，提升跟踪精度。最后，在更新阶段，采用一种以相关带为单位，根据不同权重系数进行判断的模板替换机制，以加强模板的抗干扰性。仿真结果表明，所提方法能稳定、鲁棒的跟踪到感兴趣的目标。

Mine intelligent monitoring system is the key link to guarantee the coal mine production, but it is restricted to the limited underground communication resources. In the transmission mode based on Nyquist sampling theorem, it is difficult to guarantee the quality of collected video images. However, the new transmission architecture of the compressed sensing transmission model based on sparse theory has effectively changed the situation. As an important part of compressed sensing model, sparse reconstruction plays a crucial role in imaging quality. Therefore, it is necessary to study the related technologies of mine image reconstruction under the new transmission framework. In addition, due to the particularity and complexity of underground environment, the mine monitoring system is faced with the influence of uneven light distribution, low light intensity and multi-source noise when it is working. There are many problems in traditional manual monitoring methods, monitoring efficiency and accuracy are difficult to meet the needs of coal mine safety production. So it is essential to further accelerate the application of vision technologies, in order to improve the intelligence level of monitoring system and provide more powerful guarantee for behavior analysis, identification and subsequent early warning linkage mechanism through target detection, tracking and other measures.

Based on the sparse representation theory，aiming at the problems in the mine monitoring，such as the low accuracy of image restriction，poor robustness of target detection and tracking and weak stability and so on. The performance of compressive sensing reconstruction algorithm is studied，multi-path reconstruction algorithm based on breadth and depth first and target detection, multiple observations joint sparse reconstruction algorithm based on Bayesian theory and target tracking based on sparse representation. Moreover，the paper extends the sparse representation theory to the cross-camera tracking. The main research contents are as follows：

Aiming at the decoder accompanying with disturbance and the problem of RIP performance boundary of sparse signals with multiple observations, atomic coherence is taken as the entry point in this paper. Firstly, in the single observation sparse signal model, the reconstructed RIP performance boundary of BLOOMP algorithm under the condition of complete perturbation is derived. Secondly, BLOOMP algorithm is extended to the multi-observation sparse reconstruction model, proposing the BLO-SOMP algorithm. The RIP performance boundary of the algorithm is derived to reconstruct the signal accurately under the ideal condition. The sufficient condition and reconstruction error range of the algorithm are given for accurate reconstruction signals with noise and disturbance.

The mine image reconstruction problem of single observation sparse model is studied. Aiming at the problem of low reconstruction performance of traditional multi-path algorithm, two new multi-path matching pursuit algorithms are proposed. In the proposed accelerated MMP algorithm, the correct decomposition points traversal more effective support set by using threshold and pruning tree model strategy to reduce redundant paths. The convergence condition of accelerated MMP algorithm is derived theoretically. In the proposed path adaptive matching pursuit algorithm, construct the path basement by particle swarm optimization, and design a strategy of selecting better ones increasing the number of paths gradually by combining the reconstruction coefficient. The support set is evaluated twice by regularization method to improve the support accuracy. In the standard image and mine image reconstruction experiments, the two algorithms proposed in this paper have good performance, and take into account the reconstruction efficiency.

The mine image reconstruction problem of multiple observations joint model is studied. Aiming at the problems of noise interference and unknown non-zero position of signal support set in complex environment, two new reconstruction algorithms based on Bayesian theory are proposed. In the proposed reconstruction algorithm based on maximum posterior ratio, Gauss and multivariate Laplace distributions are used to describe the sparsity between the noise source and the unknown signal respectively, and the correlation coefficient distribution model based on Gauss observation matrix is established. A new matching strategy is designed based on the maximum posterior ratio combining with the forward and backward matching pursuit algorithm, which is used to solve the optimal solution of the underdetermined equation. In the proposed reconstruction algorithm based on Bayesian hierarchical model, a hierarchical Bayesian model with structural properties is firstly established to represent the prior information of the joint signals. Secondly, multivariate matching criterion combining variational method is used to obtain the initial expectation of hidden variables, which is used as the prior information of joint support. Then, deriving the correction factor by using the obtained information, and optimize the cost function of the underdetermined equation by combining backtracking strategy. Finally, a two-stage SFBP algorithm is introduced to realize the accurate estimation of the support. In the reconstruction experiment, the two algorithms proposed in this paper have more reliable and stable reconstruction performance under the condition of unknown support position and noise interference.

Aiming at the problem of low detection accuracy caused by multi-source noise in mine target detection, a target detection model based on sparse representation is proposed. Multi-source noise is filtered by non-mean filtering technology. Background modeling is completed by using improved K-SVD dictionary, and accurate detection of targets is realized by combining with sparse representation framework. The experimental results show that the proposed algorithm can ensure the accuracy of stable detection and better adapt to the special environment in the mine. In the target tracking stage, a moving target tracking model based on sparse representation is proposed to solve the problem of low tracking accuracy caused by external interference such as illumination and noise. Firstly, the video image is normalized by illumination, and the subbands of different frequency information are obtained by wavelet transform. The high frequency part is de-noised by the weighted guided filter. Then the optimized target image is obtained by time-frequency inverse wavelet transform. Secondly, in the target reconstruction stage, a new discriminant condition is introduced to update the radius of the correlation set to obtain a more accurate support set, thus reducing the reconstruction error. Finally, in the dictionary update stage, a new monitoring mechanism is designed, which uses correlation sets to sort the similarity between the target and the discriminant template respectively, and selects the qualified atoms to replace them, so as to reduce the error accumulation. The above and below mine tracking experiments show that the algorithm presented in this paper has good performance in accuracy and robustness.

In view of the differences of the areas covered by different cameras and the randomness of the moving target behavior trajectory under the across cameras, which leading to interference error accumulation and affects matching accuracy. Aiming at the problem, a tracking model combined with sparse representation theory is proposed. Firstly, the model gives the brightness compensation formula through the background brightness values between different cameras. Secondly, BLOOMP algorithm is introduced, and a more compact correlation band is obtained by combining local optimization technology with the new coherence discrimination mechanism, so as to optimize the tracking model and improve tracking accuracy. Finally, in the updating stage, a template replacement mechanism based on different weight coefficients adopts a correlation band as a unit to enhance the anti-interference performance of the template. Simulation results show that the proposed method can track the target of interest stably and robustly.