Interferogram Interpolation Method Research on TSMFTIS based on
Kernel Regression with Relative Deviation
Fengzhen Huang*, Jingzhen Li, Jun Cao
Key Laboratory of Precision Opto-mechatronics Technology, Ministry of Education, Beijing
University of Aeronautics & Astronautics, Beijing, 100191, China
ABSTRACT
Temporally and Spatially Modulated Fourier Transform Imaging Spectrometer (TSMFTIS) is a new imaging
spectrometer without moving mirrors and slits. As applied in remote sensing, TSMFTIS needs to rely on push-broom of
the flying platform to obtain the interferogram of the target detected, and if the moving state of the flying platform
changed during the imaging process, the target interferogram picked up from the remote sensing image sequence will
deviate from the ideal interferogram, then the target spectrum recovered shall not reflect the real characteristic of the
ground target object. Therefore, in order to achieve a high precision spectrum recovery of the target detected, the
geometry position of the target point on the TSMFTIS image surface can be calculated in accordance with the sub-pixel
image registration method, and the real point interferogram of the target can be obtained with image interpolation
method. The core idea of the interpolation methods (nearest, bilinear and cubic etc) are to obtain the grey value of the
point to be interpolated by weighting the grey value of the pixel around and with the kernel function constructed by the
distance between the pixel around and the point to be interpolated. This paper adopts the gauss-based kernel regression
mode, present a kernel function that consists of the grey information making use of the relative deviation and the
distance information, then the kernel function is controlled by the deviation degree between the grey value of the pixel
around and the means value so as to adjust weights self-adaptively. The simulation adopts the partial spectrum data
obtained by the pushbroom hyperspectral imager(PHI) as the spectrum of the target, obtains the successively push-
broomed motion error image in combination with the related parameter of the actual aviation platform; then obtains the
interferogram of the target point with the above interpolation method; finally, recovers spectrogram with the nonuniform
fast Fourier transform algorithm. Compared with the accurate spectrogram, the spectrogram recovered with the relative
deviation-based kernel regression interpolation method has remarkable improvement over the previous methods.
Keywords: Temporally and Spatially Modulated Fourier Transform Imaging Spectrometer, interferogram, kernel
regression, relative deviation
1. INTRODUCTION
Imaging spectrum technique is a new detection technique, which is developed gradually from optical remote sensing, this
technique can obtain the spatial and spectral information of the ground object target simultaneously. Interference
imaging spectrometer, as an important branch of the imaging spectrum technique, has been extensively applied in the
field, such as natural disaster Surveillance, water resources and mineral resources survey. According the difference on
the interference information modulation method, interference imaging spectrometer can be divided as time-modulated
type (TMII) [1], space-modulated type (SMII) [2]and temporally and spatially modulated type (TSMFTIS) [3-5].
Wherein, TMII has moving part, thus has relative poor stability; SMII has set slit in the optical system, and the slit limits
the throughput; while, actually, TSMFTIS has added a laterally-shared beam splitter on a ordinary camera system, so the
target image obtained on the final image has interference fringe overlaid, thus TSMFTIS has the advantages of high
throughput, high stability etc and it has become the research focus of interference imaging spectrum field.
When the moving state of the TSMFTIS has changed during the imaging process, the image point of the remote sensing
image corresponding to the target deviates from the image point of the ideal motion imaging, thus leads high distortion
of the error interferogram extracted from the sequence image compared with that of the ideal interferogram, then the
recovery spectrum can not reflect the true attribute of the detail point. Thus, the motion error correction to TSMFTIS is
meaningful to the accurate spectrum recovery. While, one of the key technique to obtain the true interferogram of the
target is image interpolation, the common interpolation method (nearest, bilinear and cubic etc) adopts the distance
between the point to be interpolated and the pixel point around as the weighting value, and obtain the grey value of the
Proc. of SPIE Vol. 9449 944932-1