Error analysis for quadtree image formation

The quadtree image formation technique is a computationally efficient approximation to standard backprojection. Where the computational load of backprojection is O(N³) for N sensors forming an N×N image, the quadtree method uses a divide-and-conquer strategy similar to the fast Fourier transform (FFT) to reduce the computational load down to O(N² log(N)). However, the quadtree introduces errors in the relative time shifts used to focus pulses. These errors reduce the signal gain in the mainlobe response for isotropic point-like targets. In addition, the oscillations of the sidelobes increase from stage to stage. This paper develops performance bounds for the mainlobe losses under far field conditions and relates these bounds to the slow-time Nyquist rate