Coupled Basis Pursuit for 3D Terahertz Video Reconstruction

The emerging field of THz imaging holds great promise for diverse application fields, such as security, quality control, medical diagnosis, and bio-imaging. Due to the penetration ability of THz radiation, THz imaging is inherently 3-dimensional. This is, however, both an opportunity and a challenge, due to the sheer size of the ambient dimension that results from fine discretization of the 3D target space. Computational sensing approaches, which combine enhanced measurement diversity with tailored reconstruction methods exploiting priors such as sparsity, have emerged as a way to attain volumetric reconstruction without scanning. However, solving the resulting inverse problem becomes challenging for complex targets and high resolution. In this work, we highlight that existing methods for THz imaging leveraging priors in the 2D or 3D target space do not leverage priors along the time dimension. Under the hypothesis that variations between consecutive frames are sparse, we propose a dual-domain sparse regularization, which we recast into an augmented linearly-constrained <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\ell_{1}$</tex> minimization problem. The later jointly enforces target sparsity, as well as consistency with both the measurements and the previously reconstructed 3D frame. Comprehensive simulations confirm the ability of the proposed coupling to reduce 3D reconstruction error.