Highly-directional image artifacts such as ion mill curtaining, mechanical scratches, or image striping from beam instability degrade the interpretability of micrographs. These unwanted, aperiodic features extend the image along a primary direction and occupy a small wedge of information in Fourier space. Deleting this wedge of data replaces stripes, scratches, or curtaining, with more complex streaking and blurring artifacts-known within the tomography community as 'missing wedge' artifacts. Here, we overcome this problem by recovering the missing region using total variation minimization, which leverages image sparsity-based reconstruction techniquescolloquially referred to as compressed sensing-to reliably restore images corrupted by stripe-like features. Our approach removes beam instability, ion mill curtaining, mechanical scratches, or any stripe features and remains robust at low signal-to-noise. The success of this approach is achieved by exploiting compressed sensing's inability to recover directional structures that are highly localized and missing in Fourier Space.