Multi-Static Multi-Frequency Image Reconstruction Based on Non-Uniform FFT

Abstract

By now a considerable number of articles on the common principles and theory of radio holographic imaging of objects based on a new method of multi-static radio-holography (MRH) have been are published.In contrast to the method of image reconstruction using the classical radio holography (CRH) to have the MRH approach it is possible to use a non-equispaced antennas array with independent transmitting and receiving elements. Radio-holography samples are received for each pair of “transmitting element-receiving element”. The number of independent samples is equal to the product of the number of transmitter elements and receiver elements and may be approximately equal to the number of samples used in CRH. An additional improvement in the quality of reconstructed image for three-dimensional objects in both approaches is achieved through the use of multi-frequency radiation.The wide common method of reconstructing images from the classical radio-hologram uses algorithms of two-fold Fast Fourier Transform (FFT), while due to focusing the multi-static radio-hologram a back projection method has been used. The back projection method is timeconsuming. However, it can be transformed to the form of two-fold non-uniform FFT (NuFFT). According to data available in the foreign references a computational efficiency of NuFFT is close to the efficiency of the classical FFT on an equidistant grid sampling. In the specific antenna configuration an example of the multi-static multi-frequency focusing and image reconstruction of three dimensional model object with back projection and NuFFT approach are presented.

Keywords

• radio hologram
• image restoring
• multi-static holography
• non-uniform FFT