Vector Sparse Representation of Color Image Using Quaternion Matrix Analysis
Abstract
Traditional sparse image models treat color image pixel as a scalar, which represents color channels separately or concatenate color channels as a monochrome image.In this paper, we propose a vector sparse representation model for color images using quaternion matrix analysis.It conducts the sparse basis selection in quaternion space, which uniformly transforms the channel images to an orthogonal color space.Moreover, the proposed sparse model is more efficient comparing with the current sparse models for image restoration tasks due to lower redundancy between the atoms of different color channels. The experimental results demonstrate that the proposed sparse image model avoids the hue bias issue successfully.powerful tool in color image analysis and processing domain.
The theory of sparse representation has been proven as an effective model for image representation.
Using an overcomplete dictionary that contains a certain number of prototype atoms as its elements, an image signal can be represented as a sparse linear combination of these atoms.
Conclusion
In this Vector Sparse Representation of Color Image Using Quaternion Matrix Analysis paper.
we propose a novel sparse model for color image using quaternion matrix analysis.
It formulates a color pixel as a vector unit instead of a scalar quantity
consequently overcomes the lack of accuracy describing inter-relationship among color channels.
The experiments of reconstruction, denoising, inpainting, and super-resolution on natural color images prove its advantages in effectively accounting for both luminance and chrominance geometry in images.
We believe that the physically meaningful real part will further help us capture color information.
In the future, we will further explore the potential extension of quaternion sparse model to four-channel color space, e.g. CMYK, in which the real part may corresponds to the black channel.
