Abstract: In the research process of sampling problems, time encoding machines have been proposed as easy to implement and efficient sampling devices. In order to achieve the goal of efficient signal reconstruction, adaptive sampling and reconstruction of signals in quasi shift-invariant space based on time encoding machines are studied, with emphasis on the reconstruction algorithm of quasi shift-invariant signals. First, based on "Crossing" and "Integrated and Fire" time encoding machines, two adaptive sampling methods are considered, and corresponding exact reconstruction algorithms are established. Second, an IF sampler that can generate finite adaptive average samples is discussed, and an approximate reconstruction algorithm based on samples is given. The results show that the established exact reconstruction algorithm has exponential convergence when the density of the time encoding machines satisfies a certain attenuation property. When the generator satisfies a certain attenuation, the convergence speed of the approximate reconstruction algorithm linearly depends on the threshold parameter of the IF sampler.