Low-rank, sparse and line constrained estimation: Applications to target tracking and convergence

In this paper, the incorporation of a line constraint is considered for structured estimation. In particular, multiple forms of structure on matrices are extended from low-rank and sparsity. The line constraint is introduced via a rotation that yields a secondary low rank condition. The proposed method is applied to single object tracking in video wherein the trajectory can be parameterized as a line. The optimization is solved via the Augmented Lagrange Multiplier method. Measurable performance improvement is observed over previous background subtraction methods that do not exploit the line structure. An aggregated error is proven to converge to zero and a boundedness analysis is conducted which suggests that the iterative algorithm is convergent.