Deblurring of irregularly sampled images by TV regularization in a spline space

Restoring a regular image from irregular samples was shown feasible via quadratic regularization using Fourier and spline representations. When the image is also blurred and noisy (as is usually the case in satellite imaging) ℓ¹ regularizers (like TV) were shown most effective, but their Fourier-domain implementation has a prohibitive computational cost. We present here a new method that combines a spline representation (for speed) with TV regularization to obtain a more accurate and good-quality restored image. Extending this approach to the blurred case is not as trivial as in the Fourier representation. Indeed, in order to avoid the sampling operator to lose its sparse structure, a projection of the convolution operator on a spline space becomes necessary. Extensive experimental results with automatic regularization and stopping criteria show that our method achieves the accuracy of with much less computational cost, closer to.