Traditional color image processing techniques often treat the red, green, and blue color channels separately, leading to the loss of correlation and inter-dependency that is intrinsic to color information. This paper presents a holistic framework for color image processing by leveraging the mathematical tools of quaternion analysis. Quaternions, four-dimensional hypercomplex numbers, provide an elegant and effective way to represent color pixels in a unified vector space, where the three imaginary components naturally correspond to the RGB channels. We explore the formulation of fundamental image processing operations within this framework, including the development of quaternion-based Fourier transforms, convolution, and linear filtering. This approach inherently preserves the vector nature of color data, leading to more geometrically coherent and perceptually meaningful results. Experimental evaluations on tasks such as color image filtering, edge detection, and noise reduction demonstrate the superiority of the quaternionic approach over conventional component-wise methods, confirming its efficacy in maintaining color integrity and enhancing processing performance.