  Synthetic aperture radar (SAR) tomography (TomoSAR) retrieves
three-dimensional (3-D) information from multiple SAR images, effectively
addresses the layover problem, and has become pivotal in urban mapping.
Unmanned aerial vehicle (UAV) has gained popularity as a TomoSAR platform,
offering distinct advantages such as the ability to achieve 3-D imaging in a
single flight, cost-effectiveness, rapid deployment, and flexible trajectory
planning. The evolution of compressed sensing (CS) has led to the widespread
adoption of sparse reconstruction techniques in TomoSAR signal processing, with
a focus on $\ell _1$ norm regularization and other grid-based CS methods.
However, the discretization of illuminated scene along elevation introduces
modeling errors, resulting in reduced reconstruction accuracy, known as the
"off-grid" effect. Recent advancements have introduced gridless CS algorithms
to mitigate this issue. This paper presents an innovative gridless 3-D imaging
framework tailored for UAV-borne TomoSAR. Capitalizing on the pulse repetition
frequency (PRF) redundancy inherent in slow UAV platforms, a multiple
measurement vectors (MMV) model is constructed to enhance noise immunity
without compromising azimuth-range resolution. Given the sparsely placed array
elements due to mounting platform constraints, an atomic norm soft thresholding
algorithm is proposed for partially observed MMV, offering gridless
reconstruction capability and super-resolution. An efficient alternative
optimization algorithm is also employed to enhance computational efficiency.
Validation of the proposed framework is achieved through computer simulations
and flight experiments, affirming its efficacy in UAV-borne TomoSAR
applications.
