[6] The resolution of migration/inversion

To understand which factors influence the resolution of the migration/inversion, we analyze the following matrices:  

$$\left\lbrace \left[W^{U} \right]^{H}\left[W^{U} \right] \rig... ...\left[W^{D} \right]^{H}\left[W^{D} \right] \right\rbrace ^{-1}.$$ (90)

Ideally, all the matrices $\left\lbrace \left[W^{U} \right]^{H}\left[W^{U} \right] \right\rbrace ^{-1}$, $\left\lbrace \left[W^{U} \right]^{H}\left[W^{U} \right] \right\rbrace$, $\left\lbrace \left[W^{D} \right]^{H}\left[W^{D} \right] \right\rbrace$ and $\left\lbrace \left[W^{D} \right]^{H}\left[W^{D} \right] \right\rbrace ^{-1}$ are the identity matrix E, and at this time the image $\left[R\left(\theta \right) \right]$ is of the highest resolution. From ray theory tomography, resolution is closely related to acquisition aperture. The larger the aperture, the higher the resolution. If the matrices in equation (90) are required to be an identity, besides the aperture, the spatial and temporal sampling and the propagator also have obvious effects. Theoretically, the Hessian blurs the true image of reflectivity, and the inverse of the Hessian deblurs the blurred image. In practice, the calculation of the Hessian is affected by many factors. As a result, the imaging quality is not improved distinctly.