In this paper, we investigate the problem of reconstructing hidden trajectories from a collective of separate spatial-temporal points without ID information, given the number of hidden trajectories. The challenge is three-fold: lack of meaningful features, data sparsity, and missing trajectory links. We propose a novel approach called Hidden Trajectory Reconstruction (HTR). From an information-theoretic perspective, we devise five novel temporal features and combine them into an Latent Spatial-Temporal Feature Vector (LSTFV) to characterize the dynamics of a single spatial-temporal point. The proposed features have the potential of distinguishing spatial-temporal points between trajectories. To overcome the data sparsity, we assemble the LSTFVs to a sparse Temporal Feature Tensor (TF-Tensor) and propose an algorithm called Parallel Iterative Collaborative Approximation of Sparse Tensor (PICAST). PICAST approximates the TF-Tensor by decomposing it into a tensor product of a low-rank core identity tensor and three dense factor matrices with a divide-and-conquer strategy. To achieve a dense approximate tensor with good accuracy and efficiency, PICAST minimizes a sparsity-measure and fuses an additional matrix of static geographical region features. To recover the missing trajectory links, we propose a mapping, Cross-Temporal Connectivity Preserving Transformation (CTCPT), to map the LSTFVs of the separate spatial-temporal points to an intrinsic space called Cross-Temporal Connectivity Preserving Space (CTCPS). CTCPT uses Cross-Temporal Connectivity (CTC) to evaluate whether two spatial-temporal points belong to the same trajectory and if they do, how strong the connectivity between them is. Due to the CTCPT, the hidden trajectories can be reconstructed from clusters generated in CTCPS by a clustering algorithm. At last, the extensive experiments conducted on synthetic datasets and real datasets verify the effectiveness and efficiency of our algorithms.