如何采集数据以及如何通过采集到的数据来恢复原始信号一直是信号分析领域中的热点问题。本项目将针对无相位采样，动态采样及混合Lebesgue空间上的采样等问题展开研究。对于无相位采样，本项目主要考虑由不规则结点生成的B样条空间里的相位恢复问题，希望给出无相位采样序列所满足的具体的密度条件，并研究其稳定性及重构算法。对于动态采样问题，本项目主要考虑多个生成元生成的平移不变子空间里的一致和非一致动态采样问题及相应的相位恢复问题，并研究再生核空间里的动态采样问题。对于混合Lebesgue空间里的采样问题，本项目将研究此空间中其它形式的采样定理，包括多个生成元的周期一致采样和非一致采样，并给出混合Lebesgue空间中函数在不同情况下的重构公式与算法，最后给出相应的误差。

How to collect data and how to use the collected data to reconstruct the original signal has been the hot issue in signal analysis. The project will focus on the phaseless sampling, dynamical sampling and the sampling on mixed Lebesgue space. For phaseless sampling，the project will mainly study the phase retrieval problem in spline spaces generated by B-splines with arbitrary knots. We will give the specific density conditions for the phaseless sampling sequence, and study its stability and reconstruction algorithm. For dynamical sampling, we mainly consider the uniform and nonuniform sampling in multiply generated shift-invariant spaces and the corresponding phase retrieval problem. At the same time, we will study the dynamical sampling in reproducing kernel spaces. For the sampling in mixed Lebesgue space, the project will focus on the other forms of sampling theorem which include the periodic uniform and nonuniform sampling. We will give the reconstruction formula and algorithms for the original function, also give the reconstruction error.