An enhanced sparse representation framework incorporating CoSaMP-BLOTLESS for improved multi-focus image fusion

Abstract The efficiency of the dictionary learning and sparse recovery mechanisms plays a crucial role in sparse-representation-based image fusion. The recently proposed Block Total Least Squares (BLOTLESS) update algorithm is able to better perform dictionary learning, but it has higher computational complexity and longer dictionary learning time, which hinders its application in practice. To address this disadvantage, in this paper, we suggest a modified over the dictionary learning framework, which is modified the sparse coding stage in the BLOTLESS optimization process to overcome this disadvantage and named it CoSaMp-BLOTLESS. The proposed framework is based on an alternative sparse recovery method called CoSaMP which yields more reliable sparse coefficients prior to the dictionary update, thus improving the behaviour and computation of dictionary learning in general. Learned dictionaries are tested on a sparse representation-based multi-focus image fusion, both on gray-level and regular Lytro images. Firstly, both the standard BLOTLESS algorithm and the proposed CoSaMp-BLOTLESS algorithm are used to train the dictionaries on natural grayscale images. These learned dictionaries are then applied in a multi-focus image fusion framework based on sparseness and tested on the grayscale and standard Lytro data sets. The experimental results are then evaluated against various benchmark dictionary learning algorithms (MOD, K-SVD, SimCO, and BLOTLESS) with a number of quantitative fusion quality measures. The proposed CoSaMp-BLOTLESS algorithm reduced the dictionary learning time by around 18% without decreasing the quality performance of the fusion process in terms of Structural Similarity Index Measure (SSIM), Quantitative Assessment Based on Edge Information Preservation (Qabf), Fusion Mutual Information (FMI), and Multi-Scale Structural Similarity Index Measure (MS-SSIM). The experimental results validate the effectiveness of the proposed framework in terms of computational efficiency whilst maintaining sparse recovery quality. In conclusion, the proposed CoSaMp-BLOTLESS framework provides a good tradeoff between computational efficiency and fusion performance to perform sparse representation-based multi-focus image fusion and more generally for sparse image processing application.