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The screen content images (SCIs) usually comprise various content types with sharp edges, in which the artifacts or distortions can be well sensed by the vanilla structure similarity measurement in a full reference manner. Nonetheless, almost all of the current SOTA structure similarity metrics are "locally" formulated in a single-level manner, while the true human visual system (HVS) follows the multi-level manner, and such mismatch could eventually prevent these metrics from achieving trustworthy quality assessment. To ameliorate, this paper advocates a novel solution to measure structure similarity "globally" from the perspective of sparse representation. To perform multi-level quality assessment in accordance with the real HVS, the above-mentioned global metric will be integrated with the conventional local ones by resorting to the newly devised selective deep fusion network. To validate its efficacy and effectiveness, we have compared our method with 12 SOTA methods over two widely-used large-scale public SCI datasets, and the quantitative results indicate that our method yields significantly higher consistency with subjective quality score than the currently leading works. Both the source code and data are also publicly available to gain widespread acceptance and facilitate new advancement and its validation.