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For many years, channels of a color image have been processed individually,or the image has been converted to grayscale one with respect to color imageprocessing. Pure quaternion representation of color images solves this issue asit allows images to be processed in a holistic space. Nevertheless, it bringsadditional costs due to the extra fourth dimension. In this paper, we proposean approach for representing color images with full quaternion numbers thatenables us to process color images holistically without additional cost intime, space and computation. With taking auto- and cross-correlation of colorchannels into account, an autoencoder neural network is used to generate aglobal model for transforming a color image into a full quaternion matrix. Toevaluate the model, we use UCID dataset, and the results indicate that themodel has an acceptable performance on color images. Moreover, we propose acompression method based on the generated model and QSVD as a case study. Themethod is compared with the same compression method using pure quaternionrepresentation and is assessed with UCID dataset. The results demonstrate thatthe compression method using the proposed full quaternion representation faresbetter than the other in terms of time, quality, and size of compressed files.

Full Quaternion Representation of Color images: A Case Study on QSVD-based Color Image Compression