A two-dimensional (2D) quaternion Fourier transform (QFT) defined with the kernel is proposed. Some fundamental properties, such as convolution, Plancherel and vector differential theorems, are established. The heat equation in quaternion algebra is presented as an example of the application of the QFT to partial differential equations. The wavelet transform is extended to quaternion algebra using the kernel of the QFT.
['Mawardi Bahri', 'Ryuichi Ashino', 'Rémi Vaillancourt']
CONTINUOUS QUATERNION FOURIER AND WAVELET TRANSFORMS