  Optical flow is the pattern of apparent motion of objects in a scene. The
computation of optical flow is a critical component in numerous computer vision
tasks such as object detection, visual object tracking, and activity
recognition. Despite a lot of research, efficiently managing abrupt changes in
motion remains a challenge in motion estimation. This paper proposes novel
variational regularization methods to address this problem since they allow
combining different mathematical concepts into a joint energy minimization
framework. In this work, we incorporate concepts from signal sparsity into
variational regularization for motion estimation. The proposed regularization
uses a robust l1 norm, which promotes sparsity and handles motion
discontinuities. By using this regularization, we promote the sparsity of the
optical flow gradient. This sparsity helps recover a signal even with just a
few measurements. We explore recovering optical flow from a limited set of
linear measurements using this regularizer. Our findings show that leveraging
the sparsity of the derivatives of optical flow reduces computational
complexity and memory needs.
