Convolutional analysis operator learning for multifocus image fusion

Sparse representation (SR), convolutional sparse representation (CSR) and convolutional dictionary learning (CDL) are synthetic-based priors that have proven to be successful in signal inverse problems (such as multifocus image fusion). Unlike “synthesis” formulas, “analysis” model assigns probabilities to signals through various forward measurements of signals. Analysis operator learning (AOL) is a classical analysis-based learning method. Convolutional analysis operator learning (CAOL) is convolutional form of AOL. CAOL uses unsupervised learning method to train autocoded convolutional neural network (CNN) to more accurately solve inverse problem. From the perspective of CAOL, this paper introduces learned convolutional regularizers into multifocus image fusion and proposes CAOL-based multifocus image fusion algorithm. In the CDL stage, convergent block proximal extrapolated gradient method with majorizer (BPEG-M) and adaptive momentum restarting scheme are used. In the sparse fusion stage, alternating direction method of multipliers (ADMM) approach with convolutional basis pursuit denoising (CBPDN) and l1 norm maximum strategy are employed for high-frequency and low-frequency component, respectively. 3 types of multifocus images (static gray images, gray images in sports and color images) are tested to verify performance of the proposed method. A comparison with representative methods demonstrates superiority of our method in terms of subjective observation and objective evaluation. •A new multi-focus image fusion framework CAOL-based is proposed.•The different rules are used to alleviate fusion defect of connection areas.•The fusion performance under different filters with CAOL is discussed.