本发明涉及基于字典学习和稀疏表示的欠采样信号高分辨率重构方法，解决了欠采样信号中高频成分丢失及信号采集过程中受外界环境影响等问题，该方法主要包含训练和测试重构两个阶段。前者主要通过稀疏表示模型对大量训练数据进行字典训练，建立包含高低分辨率信号特征信息的字典对，后者使用字典对和稀疏编码对低分辨率信号完成信号重建过程。本发明为最大程度获得低分辨率信号的特征信息、优化字典训练的可靠性，对低分辨率信号进行离散小波变换作为信号的预处理方法。作为本发明提出的方法易于实现、运行时间短、重构效率高，利用稀疏表示的相似性不仅减少了低采样率信号对重构效果的影响，也成功估计出欠采样信号中丢失的频率成分。

The invention relates to a high-resolution reconstruction method of under-sampled signals based on dictionary learning and sparse representation, which solves the problems of loss of high-frequency components in under-sampled signals and the influence of external environment in the signal acquisition process, etc. The method mainly includes two stages of training and test reconstruction. The former mainly trains a large number of training data by dictionary through sparse representation model, and establishes dictionary pairs containing the characteristic information of high and low resolution signals. The latter uses dictionary pairs and sparse coding to complete the signal reconstruction process of low resolution signals. In order to obtain the characteristic information of the low-resolution signal to the greatest extent and optimize the reliability of dictionary training, the invention performs discrete wavelet transform on the low-resolution signal as a signal preprocessing method. The method provided by the invention is easy to implement, short in running time and high in reconstruction efficiency, and the similarity of sparse representation not only reduces the influence of low sampling rate signals on reconstruction effect, but also successfully estimates the lost frequency components in undersampled signals.