Iterative adaptive extrapolation applied to SAR image formation and sinusoidal recovery

Alejandro Enrique Brito, University of Texas at El Paso


The adaptive weighted norm extrapolation (AWNE) algorithm is evaluated as a superresolution method for SAR image formation and a two-dimensional extension is devised to overcome some of the limitations encountered with the existing one-dimensional version. Subsequently, AWNE is analyzed, improved and reformulated for harmonic signals. Particularly, the AWNE output is statistically characterized under noise and noise-free conditions as a windowed version of the true harmonic signal and the accuracy of the modeling assumption is verified experimentally. Then, a theoretical derivation of this imposed window is carried out for sinusoids to corroborate with the empirical models under certain conditions. Next, two improvements to allow for perfect recovery of harmonic signals are devised. The first one undoes the windowing effect by allowing unrestricted extrapolation lengths that flatten the imposed window. The second improvement is based on the pursuit of the autocorrelation (zero-phase version) of the true signal to produce a linear expansion for exact recovery. A method to correctly find the ideal autocorrelation leads to the use of circular convolution operations. The new algorithm called circular convolution AWNE (CCAWNE) presents perfect recovery capabilities for sinusoids on the associated DFT grid. ^ Working directly in the frequency domain, a new version of the CCAWNE algorithm is devised under an iterative reweighted (IRW) framework and is shown to be an optimal basis selection method. The IRW's relation with other methods such as FOCUSS and affine scaling transformation based methods is formally established including convergence properties. The unification of various methods under a generalized basis selection (GBS) principle for efficient representation of harmonic signals using Fourier dictionaries leads to the generation of a family of sparse solutions through minimization of the lp norm (1 ≤ p < 2) and lp-norm-like diversity measures (0 ≤ p < 1). ^ Finally, a novel method denoted iterative reweighted minimal solver (IRMS) is derived to solve the lp minimization problem associated with the GBS principle in the range (1 < p < 2). The IRMS method is based on the reformulation of the GBS constrained minimization problem that is solved via the iterative reweighted least squares algorithm. Refinement strategies to adaptively increase the resolution of the Fourier dictionaries are then illustrated. ^

Subject Area

Engineering, Electronics and Electrical

Recommended Citation

Brito, Alejandro Enrique, "Iterative adaptive extrapolation applied to SAR image formation and sinusoidal recovery" (2001). ETD Collection for University of Texas, El Paso. AAI3023413.