In this paper, the problem of non-rigid structure estimation in trajectory space from monocular vision is investigated. Similar to the Point Trajectory Approach (PTA), based on characteristic points’ trajectories described by a predefined Discrete Cosine Transform (DCT) basis, the structure matrix was also calculated by using a factorization method. To further optimize the non-rigid structure estimation from monocular vision, the rank minimization problem about structure matrix is proposed to implement the non-rigid structure estimation by introducing the basic low-rank condition. Moreover, the Accelerated Proximal Gradient (APG) algorithm is proposed to solve the rank minimization problem, and the initial structure matrix calculated by the PTA method is optimized. The APG algorithm can converge to efficient solutions quickly and lessen the reconstruction error obviously. The reconstruction results of real image sequences indicate that the proposed approach runs reliably, and effectively improves the accuracy of non-rigid structure estimation from monocular vision.

Compressed Sensing MR imaging (CS-MRI) is one of the most promising approaches to reconstruct the MR image from highly under-sampled k-space data, while greatly reducing scanning time. Total variation (TV) is commonly used as a penalty in sparse signal recovery. In this paper, an extension of TV, termed Group-Sparse Total Variation (GSTV), is employed as a regularization term for the CS-MR image reconstruction. Three different types of MR images with two different sampling trajectories are used to validate the performance of the proposed method in reconstruction accuracy and computational efficiency. Compared with the patch-based nonlocal Operator (PANO) method, the proposed GSTV-based regularization method achieves comparable SNR but owns the advantage of faster computation. Moreover, the proposed method can obviously improve the reconstruction quality with higher signal-to-noise ratio (SNR) than the Wavelet tree sparsity method (WaTMRI), however it takes some more reconstruction time. In all, the proposed method provides a simple and effective alternative solution to the CS-MRI regularization framework.

Trajectory space model has been proposed to recover the 3D non-rigid structure from motion (NRSfM). This paper mainly did two things to improve the accuracy in NRSfM. One thing is that a sparse approximation method was introduced to recover the non-rigid structure from motion. Second, considering the advantage of the sparse approximation method in solving two incoherent basis transforms, the integration basis dictionary of DCT and Walsh-Hadamard transform (WHT) decomposition techniques was used in the paper. Experimental results showed that the mixed basis atom dictionary was more effective than any single basis dictionary in dealing with NRSfM problem. This paper not only gave out some inspiration about basis selection in sparse approximation method but also proposed a simple but effective solution for NRSfM problem.