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In this article, a detailed survey of the quantum approach to image processing is presented. Recently, it has been established that existing quantum algorithms are applicable to image processing tasks allowing quantum informational models of classical image processing. However, efforts continue in identifying the diversity of its applicability in various image processing domains. Here, in addition to reviewing some of the critical image processing applications that quantum mechanics have targeted, such as denoising, edge detection, image storage, retrieval, and compression, this study will also highlight the complexities in transitioning from the classical to the quantum domain. This article shall establish theoretical fundamentals, analyze performance and evaluation, draw key statistical evidence to support claims, and provide recommendations based on published literature mostly during the period from 2010 to 2015.