Image reconstruction from sparse data is one of the key technologies in physical imaging, and it can often be mathematically described as an underdetermined linear inverse problem. Mathematical models for sparse reconstruction often choose the sparseness constraints or data fidelity term directly as objective functions. However, physics concepts and laws for these modeling or solving processes have never been explored. In this paper, sparse reconstruction is investigated for the first time from the perspective of physical motion. Firstly, a physical model is created to describe a particle motion in viscous medium, in which the particle gravity potential energy function is the norm of l2-l1 after the relaxation transformation. In discrete calculations, the particle displacement is determined by the corresponding iterative result, and its velocity can be described as the change between two adjacent iterations. Then, a new mathematical model based on the physical motion model is studied for sparse reconstruction, in which the total energy of particle is chosen as a new objective function and nonnegative displacements as constraints. This new model preserves sparse constrains and fidelity term of original l2-l1 model, and adds the constrains of deviations between two adjacent iterations so as to avoid oscillations caused by large deviations. Furthermore, a targeted gradient projection technique is adopted to solve such a reconstruction model, and its convergence is discussed as well. Especially in this algorithm, the gradient of this new objective function contains the iterative step of previous iteration, and such iterative steps play the role of physical inertia property in iterative process, which can effectively enlarge the iterative steps to accelerate the convergence and avoid local optima. Finally, two sets of experimental results are presented, including natural grayscale image reconstruction and micro focus X-ray defect detection in precision electronic package. The results demonstrate that the proposed method outperforms its competitors distinctly in time efficiency on the basis of guaranteeing the reconstruction quality. Additionally, on detecting internal defects in solder joint of integrated circuit, the proposed method is well performed in retaining edge details of the reconstructed micro focus X-ray images. Therefore, the proposed method can identify the solder joint internal defects more accurately and is more suitable to rapid and precise micro focus X-ray defect detection in industry.