  Higher-order singular value decomposition (HOSVD) is one of the most
efficient tensor decomposition techniques. It has the salient ability to
represent high_dimensional data and extract features. In more recent years, the
quaternion has proven to be a very suitable tool for color pixel representation
as it can well preserve cross-channel correlation of color channels. Motivated
by the advantages of the HOSVD and the quaternion tool, in this paper, we
generalize the HOSVD to the quaternion domain and define quaternion-based HOSVD
(QHOSVD). Due to the non-commutability of quaternion multiplication, QHOSVD is
not a trivial extension of the HOSVD. They have similar but different
calculation procedures. The defined QHOSVD can be widely used in various visual
data processing with color pixels. In this paper, we present two applications
of the defined QHOSVD in color image processing: multi_focus color image fusion
and color image denoising. The experimental results on the two applications
respectively demonstrate the competitive performance of the proposed methods
over some existing ones.
