In this study, an efficient multifocus image fusion and reconstruction framework based on compressed sensing in the wavelet domain are proposed. The new framework is composed of three phases. Firstly, the source images are represented with their sparse coefficients using the discrete wavelet transform (DWT). Secondly, the measurements are obtained by the random Gaussian matrix from their sparse coefficients, and are then fused by the proposed adaptive local energy metrics (ALEM) fusion scheme. Finally, a fast continuous linearised augmented Lagrangian method (FCLALM) is proposed to reconstruct the sparse coefficients from the fused measurement, which will be converted by the inverse DWT (IDWT) to the fused image. Our experimental results show that the proposed ALEM image fusion scheme can achieve a higher fusion quality than some existing fusion schemes. In addition, the proposed FCLALM reconstruction algorithm has a higher peak-signal-to-noise ratio and a faster convergence rate as compared with some existing reconstruction methods.
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