Name
Abstract | ||
|---|---|---|
Quaternion matrices are employed successfully in many color image processing applications. In particular, a pure quaternion matrix can be used to represent red, green, and blue channels of color images. A low-rank approximation for a pure quaternion matrix can be obtained by using the quaternion singular value decomposition. However, this approximation is not optimal in the sense that the resulting low-rank approximation matrix may not be pure quaternion, i.e., the low-rank matrix contains a real component which is not useful for the representation of a color image. The main contribution of this paper is to find an optimal rank-r pure quaternion matrix approximation for a pure quaternion matrix (a color image). Our idea is to use a projection on a low-rank quaternion matrix manifold and a projection on a quaternion matrix with zero real component, and develop an alternating projections algorithm to find such optimal low-rank pure quaternion matrix approximation. The convergence of the projection algorithm can be established by showing that the low-rank quaternion matrix manifold and the zero real component quaternion matrix manifold has a nontrivial intersection point. Numerical examples on synthetic pure quaternion matrices and color images are presented to illustrate the projection algorithm can find optimal low-rank pure quaternion approximation for pure quaternion matrices or color images. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1137/19M1307329 | SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS |
Keywords | DocType | Volume |
color images, pure quaternion matrices, low-rank approximation, manifolds | Journal | 42 |
Issue | ISSN | Citations |
1 | 0895-4798 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Guang-Jing Song | 1 | 45 | 7.06 |
| Weiyang Ding | 2 | 1 | 0.69 |
| Ng Michael | 3 | 4231 | 311.70 |