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Quaternion K-SVD for Color Image Denoising

Amit Carmeli

Supervised by Javier Turek


In this work, we introduce the use of Quaternions within the field of sparse and redundant representations. The Quaternion space is an extension of the complex space, where each element is composed of four parts - a real-part and three imaginary parts. The major difference between Quaternion space and the complex space is that the Quaternion space has non-commutative multiplication. We design and implement Quaternion variants of state-of-the-art algorithms OMP and KSVD. We show various results, previously established only for the real or complex spaces, and use them to devise the Quaternion K-SVD algorithm, nicknamed QK-SVD. Finally, we discuss the use of QK-SVD for the purpose of color image denoising, and compare the achieved results with other work in the field.

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