Low Rank Pure Quaternion Approximation for Pure Quaternion Matrices

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 images. A low-rank approximation for obtained by using the singular value decomposition. However, this is not optimal sense that resulting may quaternion, i.e., contains real component which useful representation image. The main contribution paper find an rank-$r$ (a image). Our idea use projection on manifold with zero component, develop alternating projections algorithm such approximation. convergence established showing has nontrivial intersection point. Numerical examples synthetic images presented illustrate or