Abstract
This is a theoretical study on the minimizers of cost-functions composed of an ℓ2 data-fidelity term and a possibly nonsmooth or nonconvex regularization term acting on the differences or the discrete gradients of the image or the signal to restore. More precisely, we derive general nonasymptotic analytical bounds characterizing the local and the global minimizers of these cost-functions. We provide several bounds relevant to the observation model. For edge-preserving regularization, we exhibit a tight bound on the ℓ ∞ norm of the residual (the error) that is independent of the data, even if its ℓ2 norm is being minimized. Then we focus on the smoothing incurred by the (local) minimizers in terms of the differences or the discrete gradient of the restored image (or signal).
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Nikolova, M. (2007). Bounds on the Minimizers of (nonconvex) Regularized Least-Squares. In: Sgallari, F., Murli, A., Paragios, N. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2007. Lecture Notes in Computer Science, vol 4485. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72823-8_43
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DOI: https://doi.org/10.1007/978-3-540-72823-8_43
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72822-1
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