With the increasing threat of terrorism in recent years, the detection of concealed weapons, plastic bombs and other contraband at secure locations attracts more and more countries' attention all over the world. Three-dimensional (3D) microwave imaging surveillance systems, allowing for acquisition of full 3D microwave images of human body, have been developed for security applications. In this paper, we firstly propose a 3D imaging algorithm which not only accounts for the free space propagation losses and wavefront curvature but also avoids 3D interpolation in the 3D wavenumber domain without suffering from any approximations and truncation errors. Then, the sampling constraints and the resolution issues associated with proper and alias-free implementation of the 3D reconstruction are analyzed. Finally, the focusing capabilities of our proposed imaging algorithm are investigated and verified by means of numerical simulations as well as theoretical analysis, and an approach for better displaying projected images is examined.

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Abstract-This paper presents an improved polar format algorithm (PFA) for geosynchronous synthetic aperture radar which undergoes a near-circular track (GeoCSAR). GeoCSAR imaging geometry and signal formulation considering orbit perturbations were derived to ensure accurate slant range between antenna and targets. The illuminated area is more than one million square kilometers due to the long slant distance, resulting in large amount of data to be processed and that the scene is a spherical crown rather than a plane. By assuming spherical wavefronts instead of planar wavefronts, improved polar format algorithm (PFA) was proposed to focus GeoCSAR raw data on a spherical reference surface (ground surface), so that the size of focused scene is no longer limited by the range curvature phase error. Thus, this method could deal with large area imaging for GeoCSAR precisely and efficiently. The implementation procedure, computational complexity, phase error and achievable resolution were presented to show the focusing capabilities of this imaging algorithm. Numerical simulation was further performed to validate the feasibility of this imaging algorithm and the correctness of analysis.

In this paper, the existence and the uniqueness of the global generalized solution and the global classical solution for the initial boundary value problem of the generalized cubic double dispersion equation are proved. The nonexistence of global solution for the initial boundary value problem of the generalized cubic double dispersion equation is discussed.

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