SUPERRESOLUTION ISAR IMAGING USING 2-D AUTOREGRESSIVE LATTICE FILTERS Is ¸in Erer 1 and Ahmet Hamdi Kayran 1 1 Faculty of Electronics and Electrical Engineering Istanbul Technical University 80626, Maslak, Istanbul, Turkey Recei  ed 18 July 2001 ABSTRACT: A new efficient algorithm to obtain high-resolution ISAR images in the case of limited frequency band and small angular section ( ) is presented. The method is based on the two-dimensional 2-D autore- gressi  e modeling of 2-D Cartesian frequency backscattered data using 2-D orthogonal lattice filters. ISAR images obtained for an experimental target are included to  alidate this technique.  2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 32: 8185, 2002. Key words: ISAR imaging; lattice filters; linear prediction; autoregressi  e modeling DOI 10.1002  mop.10096 I. INTRODUCTION Classical methods based on the 2-D inverse Fourier trans- Ž . form IFT of 2-D Cartesian backscattered data are preferred over model-based techniques if the whole frequency band   and the angular section are available 1  2 . However, in many practical applications, the radar system has a limited fre- Ž . quency band reducing range resolution or the target can Ž only be observed over a small angular section reducing . cross-range resolution . This leads to radar images with lim- ited resolution. In order to increase the resolution available from the frequency- and angle-limited data, linear prediction tech- niques have been used in many studies to construct sharp   images 3  5 . However, these approaches were specifically based on 1-D spectral estimation techniques, and apply only the advantageous properties of superresolution in one of the two dimensions. Thus, the backscattered data must be col- lected over a large angular sector or the imaging system must have a large bandwidth. Recently, the 2-D modeling of the 2-D Cartesian frequency spectra using 2-D linear prediction  was proposed 6 . This method combined 2-D forward and Ž . backward prediction with singular value decomposition SVD to improve the resolution. Four different quarter-plane 2-D AR models are used to estimate the backscattered fields of the target. The unknown model coefficients are found by solving two sets of equations using SVD. It is shown that this algorithm provides much better resolution than the ISAR image obtained using a 2-D IFT. However, the performance of the SVD depends on the correct distinction between the number of eigenvalues of the correlation matrix related to  the backscattered data and the measurement noise 6 . In practice, the number of eigenvalues representing backscat- tered data equals the number of scattering centers. When there is no a priori information about the target, such as the number of scattering centers, and the distinction between the eigenvalues is not obvious, an information-based criterion  must be used 7 . Moreover, two different sets of equations must be separately solved, and for each prediction order value, these equation sets must be reformulated. In this paper, we propose a new algorithm that eliminates  the disadvantages of the 2-D linear prediction technique 6. The algorithm is based on a complex version of orthogonal  2-D lattice modeling 8 . 2-D Cartesian backscattered com- plex valued data are modeled using four quarter-plane 2-D AR models. Instead of solving two different sets of linear equations by pseudoinverse matrix inversion techniques or the SVD algorithm, a single autoregressive lattice structure is used to model the backscattered data for four quarters. By appropriately choosing the ordering in the prediction region, a lattice filter enables parallel computation of the forward and backward prediction error filter coefficients recursively in the same structure. In Section II, a high-resolution ISAR imaging algorithm based on 2-D complex lattice modeling of the backscattered data is presented. Section III contains some sample results, and conclusions are given in section IV. II. PROPOSED IMAGING ALGORITHM In the high-frequency region, a radar target can be consid- ered as a collection of a finite number of scattering centers and scattering center interactions. The coherent scattered signal from such a target can be represented as the sum of   complex scattered signals from each scattering center 1, 6 . The geometry of the imaging system for a target represented by K discrete scattering centers is shown in Figure 1. The target area is illuminated by a radar antenna, which transmits a sinusoidal waveform with a carrier frequency f . The backscattered field due to the k th scattering center at an aspect angle  and frequency f can be written in the Carte- sian frequency domain as Ž . Ž . j4  cŽ f x x k f y y k . Ž. E f , f  A f , f e 1 k x y k x y Ž . where f  f cos  , f  f sin  , A f , f is the backscat- x y k x y tered field of the k th scattering center assumed to be located on reference point, and c is the velocity of light. To obtain Ž . the scattered field for equal intervals in the f , f domain, x y the measured data can be interpolated. Cartesian frequency samples are given by Ž . Ž. Ž . Ž. f k  f 0  k  f and f k  f 0  k  f , x 1 x 1 x y 2 y 2 y Ž. k , k  0,1,2,..., N 2 1 2 Ž. Ž. where f 0 and f 0 are the initial values and  f is the x y Ž. Ž. increment. Substituting Eq. 2 into Eq. 1 , the scattered field can be expressed by equally spaced Cartesian frequency Ž . samples Ek , k . Since the bandwidth and angular region of 1 2 θ x y (range) (cross range) • Reference point Target area 1 2 k incident wavefront k th scattering center (x k ,y k ) Figure 1 Geometry of the imaging system MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 32, No. 1, January 5 2002 81