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In recent years, boundary problems associated to image restoration have attracted the attention of imaging scientists. We explore here the scenario of arbitrary boundary shapes (exemplified by blurred-background images), starting from a general discussion and advancing towards realist conditions, with simulations and real photographic images. We describe our Spectral-Pre-Adaptation (SPA) method, and compare it to the highly successful unconstrained boundary conditions Alternating Direction Method of Multipliers (UBC ADMM) method. Preliminary results indicate that SPA, combined with highly efficient restoration algorithms, such as Constrained Dynamic (ConDy) L2-relaxed L0, may set the new state-ofthe-art (in performance and computational efficiency) for this kind of problems.

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