One of the most important issues for researchers developing image processing algorithms is image quality. Methodical quality evaluation, by showing images to several human observers, is slow, expensive, and highly subjective. On the other hand, a visual quality matrix (VQM) is a fast, cheap, and objective tool for evaluating image quality. Although most VQMs are good in predicting the quality of an image degraded by a single degradation, they poorly perform for a combination of two degradations. An example for such degradation is the color crosstalk (CTK) effect, which introduces blur with desaturation. CTK is expected to become a bigger issue in image quality as the industry moves toward smaller sensors. In this paper, we will develop a VQM that will be able to better evaluate the quality of an image degraded by a combined blur/desaturation degradation and perform as well as other VQMs on single degradations such as blur, compression, and noise. We show why standard scalar techniques are insufficient to measure a combined blur/desaturation degradation and explain why a vectorial approach is better suited. We introduce quaternion image processing (QIP), which is a true vectorial approach and has many uses in the fields of physics and engineering. Our new VQM is a vectorial expansion of structure similarity using QIP, which gave it its name-Quaternion Structural SIMilarity (QSSIM). We built a new database of a combined blur/desaturation degradation and conducted a quality survey with human subjects. An extensive comparison between QSSIM and other VQMs on several image quality databases-including our new database-shows the superiority of this new approach in predicting visual quality of color images.