Adherent cells exert traction forces on their substrate, and these forces play important roles in biological functions such as mechanosensing, cell differentiation and cancer invasion. The method of choice to assess these active forces is traction force microscopy (TFM). Despite recent advances, TFM remains highly sensitive to measurement noise and exhibits limited spatial resolution. To improve the resolution and noise robustness of TFM, here we adapt techniques from compressed sensing (CS) to the reconstruction of the traction field from the substrate displacement field. CS enables the recovery of sparse signals at higher resolution from lower resolution data. Focal adhesions (FAs) of adherent cells are spatially sparse implying that traction fields are also sparse. Here we show, by simulation and by experiment, that the CS approach enables circumventing the Nyquist-Shannon sampling theorem to faithfully reconstruct the traction field at a higher resolution than that of the displacement field. This allows reaching state-of-the-art resolution using only a medium magnification objective. We also find that CS improves reconstruction quality in the presence of noise. Statement of Significance A great scientific advance of the past decade is the recognition that physical forces determine an increasing list of biological processes. Traction force microscopy which measures the forces that cells exert on their surroundings has seen significant recent improvements, however the technique remains sensitive to measurement noise and severely limited in spatial resolution. We exploit the fact that the force fields are sparse to boost the spatial resolution and noise robustness by applying ideas from compressed sensing. The novel method allows high resolution on a larger field of view. This may in turn allow better understanding of the cell forces at the multicellular level, which are known to be important in wound healing and cancer invasion.