Super-resolved Traction Force Microscopy over whole cells

Traction Force Microscopy (TFM) is a commonly used technique to compute cellular tractions that cells exert to the surrounding substrate. Traction recovery is an ill-posed inverse problem, which needs regularization to stabilize the solution. Due to its simplicity, Tikhonov or L₂-regularization is usually used, but recent studies have demonstrated the increase of sensitivity and resolution in the recovered tractions using an L₁-regularization scheme. In this manuscript, we present an approximation that makes feasible the traction recovery on full-size microscope images when working in the spatial domain. We perform also a comparison between the two regularization schemes named before (relying in L₂-norm for the data fidelity term) and the full L₁-regularization (using L₁-norm for both the regularization and data fidelity terms). Our proof of concept using real data reveal that L₁-regularizations might give an improved resolution (more accused for full L₁-regularization) and a reduction in the background noise with respect to the classical zero-order Tikhonov regularization.