Radix-$N$ Resolution-Fusion for LASAR via Orthogonal Complement Decomposition

This letter concerns the resolution-fusion method for linear array 3-D imaging SAR (LASAR). Limited by the length of the linear array, the cross-track resolution of LASAR is often lower than that in the along-track direction. To overcome this disadvantage, we assume that there are two LASAR systems whose trajectories are orthogonal to each other. Thus, we obtain a row low-resolution image and a column low-resolution image of the same scene. Using the orthogonal complement decomposition technique, we fuse the two images into one quasi-high-resolution image. Moreover, we find that the fusion distortion is unavoidable and contains the high-frequency component in both row and column directions. The information loss ratio is (
N
- 1)
²
/
N

²
(
N
denotes the ratio of low resolution to high resolution). For a smooth image, the energy loss ratio is near to zero. With the increase of the noise energy, the energy loss ratio increases correspondingly. When the noise submerges the image completely, the energy loss ratio converges to the information loss ratio.