  In recent years, Low Earth Orbit (LEO) satellites have witnessed rapid
development, with inference based on Deep Neural Network (DNN) models emerging
as the prevailing technology for remote sensing satellite image recognition.
However, the substantial computation capability and energy demands of DNN
models, coupled with the instability of the satellite-ground link, pose
significant challenges, burdening satellites with limited power intake and
hindering the timely completion of tasks. Existing approaches, such as
transmitting all images to the ground for processing or executing DNN models on
the satellite, is unable to effectively address this issue. By exploiting the
internal hierarchical structure of DNNs and treating each layer as an
independent subtask, we propose a satellite-ground collaborative computation
partial offloading approach to address this challenge. We formulate the problem
of minimizing the inference task execution time and onboard energy consumption
through offloading as an integer linear programming (ILP) model. The complexity
in solving the problem arises from the combinatorial explosion in the discrete
solution space. To address this, we have designed an improved optimization
algorithm based on branch and bound. Simulation results illustrate that,
compared to the existing approaches, our algorithm improve the performance by
10%-18%
