Most nonrigid motions use shape-based methods to solve the problem; however, the use of discrete cosine transform trajectory-based methods to solve the nonrigid motion problem is also very prominent. The signal undergoes discrete transformation due to the transform characteristics of the discrete cosine transform. The correlation of the data is well extracted such that a better compression of data is achieved. However, it is important to select the number and sequence of discrete cosine transform trajectory basis appropriately. The error of reconstruction and operational costs will increase for a high value of K (number of trajectory basis). On the other hand, a lower value of K would lead to the exclusion of information components. This will lead to poor accuracy as the structure of the object cannot be fully represented. When the number of trajectory basis is determined, the combination form has a considerable influence on the reconstruction algorithm. This article selects an appropriate number and combination of trajectory basis by analyzing the spectrum of re-projection errors and realizes the automatic selection of trajectory basis. Then, combining with the probability framework of normal distribution of a low-order model matrix, the energy information of the high-frequency part is retained, which not only helps maintain accuracy but also improves reconstruction efficiency. The proposed method can be used to reconstruct the three-dimensional structure of sparse data under more precise prior conditions and lower computational costs.