NMR spectroscopy is one of the basic tools for molecular structure elucidation. Unfortunately, the resolution of the spectra is often limited by inter-nuclear couplings. The existing workarounds often alleviate the problem by trading it for another deficiency, such as spectral artefacts or difficult sample preparation and, thus, are rarely used. We suggest an approach using the coupling deconvolution in the framework of compressed sensing (CS) spectra processing that leads to a major increase in resolution, sensitivity, and overall quality of NUS reconstruction. A new mathematical description of the decoupling by deconvolution explains the effects of thermal noise and reveals a relation with the underlying assumption of the CS. The gain in resolution and sensitivity for challenging molecular systems is demonstrated for the key HNCA experiment used for protein backbone assignment applied to two large proteins: intrinsically disordered 441-residue Tau and a 509-residue globular bacteriophytochrome fragment. The approach will be valuable in a multitude of chemistry applications, where NMR experiments are compromised by the homonuclear scalar coupling.