Abstract. Acquired digital images are often corrupted by a lack of camera focus, faulty illumination, or missing data. An algorithm is presented for fusion of multiple corrupted images of a scene using the lifting wavelet transform. The method employs adaptive fusion arithmetic based on matrix completion and self-adaptive regional variance estimation. Characteristics of the wavelet coefficients are used to adaptively select fusion rules. Robust principal component analysis is applied to low-frequency image components, and regional variance estimation is applied to high-frequency components. Experiments reveal that the method is effective for multifocus, visible-light, and infrared image fusion. Compared with traditional algorithms, the new algorithm not only increases the amount of preserved information and clarity but also improves robustness. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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System models that are linear in parametric structure, but arbitrarily nonlinear in signal operations, are identified using an approach with two novel components. The fundamental parameter estimation task (the "linear" part) uses a set-theoretic analysis of the data to deduce feasible sets of solutions in light of certain model assumptions. In turn, measurable set solution properties are used to assess the viability of nonlinear regressor functions that compete for "survival" as components of the model best fit to represent the system. The solution is formulated as a somewhat unconventional exercise in evolutionary computation.