We use least-squares migration to emphasize edge diffractions. The inverted forward modeling operator is the chain of three operators: Kirchhoff modeling, azimuthal plane-wave destruction and path-summation integral filter. Azimuthal plane-wave destruction removes reflected energy without damaging edge diffraction signatures. Path-summation integral guides the inversion towards probable diffraction locations. We combine sparsity constraints and anisotropic smoothing in the form of shaping regularization to highlight edge diffractions. Anisotropic smoothing enforces continuity along edges. Sparsity constraints emphasize diffractions perpendicular to edges and have a denoising effect. Synthetic and field data examples illustrate the effectiveness of the proposed approach in denoising and highlighting edge diffractions, such as channel edges and faults.