Multiscale transform (MST) and sparse representation (SR)-based image fusion techniques are widely used in many applications. However, the existing fusion methods are inefficient to perfectly seize significant details and texture information of input images because of some limitations of MST- and SR-based techniques. Moreover, it is quite important to measure singularities and structural information of the fused image to objectively measure the performance of different fusion techniques. Therefore, a metric which can efficiently measure singularity and structural information of the fused image would be quite useful for comparison of different fusion techniques. To address these issues, a modified Meyer windowbased adjustable nonsubsampled shearlet transform (ANSST) is proposed for decomposition of preregistered input images into lowand high-frequency coefficients. The low-frequency bands are fused by convolutional SR modeling. The high-frequency bands are fused by our proposed information entropy, standard deviation, and range descriptor, which considers entropy, standard deviation, and range-filtering features. Moreover, a metric Q_SS is formulated to measure the singularities and structural information of the fused image. The Q_SS metric is developed by using the concept of the proposed native division and native difference filtering. To show the applicability of the proposed image framework, the proposed ANSST is applied for image denoising. Experimental results verify the effectiveness of the proposed fusion method and the metric Q_SS.