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Recently, falsified images have been found in papers involved in research misconducts. However, although there have been many image forgery detection methods, none of them was designed for molecular-biological experiment images. In this paper, we proposed a fast blind inquiry method, named FBI$_{GEL}$, for integrity of images obtained from two common sorts of molecular experiments, i.e., western blot (WB) and polymerase chain reaction (PCR). Based on an optimized pseudo-background capable of highlighting local residues, FBI$_{GEL}$ can reveal traceable vestiges suggesting inappropriate local modifications on WB/PCR images. Additionally, because the optimized pseudo-background is derived according to a closed-form solution, FBI$_{GEL}$ is computationally efficient and thus suitable for large scale inquiry tasks for WB/PCR image integrity. We applied FBI$_{GEL}$ on several papers questioned by the public on \textbf{PUBPEER}, and our results show that figures of those papers indeed contain doubtful unnatural patterns., Comment: This version is an extension of Prof. Shao's previous conference paper (IEEE GlobalSIP 2018): "Unveiling Vestiges of Man-Made Modifications on Molecular-Biological Experiment Images." (https://doi.org/10.1109/GlobalSIP.2018.8646594)