# A Wide-Area Deep Ocean Floor Mapping System: Design and Sea Tests
## Appendix B High Sidelobe Effects in a Sparse Array Image and Reduction Algorithm Development
### Sidelobe-Reduction Algorithm Development  
We are developing algorithms to reduce sidelobe artifacts and improve image quality. We briefly describe the present algorithm and demonstrate its performance for a simple simulated case.  
Our algorithm shares a similar philosophy with the alternative projection [14] that is widely used in passive sonar applications. Both algorithms estimate a single-point source and its waveform at each iteration. Alternative projection estimates the signal waveform of a point source as the entire component contained in its estimated direction. Estimating the waveform with a single step can cause energy smearing from nearby sources. Imaging a cluttered region with a sparse array system with typically high sidelobe levels can suffer from energy smearing from other sources or background noise and severely contaminate the waveform estimate. Our algorithm partially estimates the underlying point source's waveform at each iteration. The estimation is less susceptible to contamination by other point sources or background noise, as sidelobe leakage from neighboring sources also decreases as iterations progress.  
The iterative scheme we implement is inspired by the CLEAN algorithm of [PERSON] [29], which is commonly used for long-baseline astronomical interferometry. However, our deconvolution algorithm is different from the original CLEAN algorithm. The CLEAN algorithm was originally developed based on the van Certtite-Zernike theorem [45, 46]. It uses the duality property of the cross-correlation of the electric field measured at two distinct points, i.e., visibility and directional spectral density. The CLEAN algorithm operates on the second-moment statistics and removes sidelobe power artifacts. Our algorithm uses the direct acoustic pressure field and estimates the location and waveform of underlying point sources to remove the sidelobe field artifacts.  
Our algorithm starts with matched filtering, followed by beamforming the received signal. This coherent processing is typically performed in the complex baseband for computational efficiency, and, as a result, the raw processed outputs are also complex values. The order of matched filtering and beamforming are interchangeable because both processes are linear. It is, however, computationally efficient to first matched filter the element time series when the number of voxels exceeds the number of \"receive\" elements. We define the raw complex output of the coherent processing as the \"complex dirty map\", following the terminology in the original CLEAN algorithm [29]. The algorithm then finds the power peak location in the dirty map and calculates the complex point response function at that peak location. The complex point response function is defined as the \"complex dirty beam\". The peak height of the complex dirty beam is scaled by 10-25% of the dirty map power peak strength with a phase identical to the complex dirty map peak. This scaled, phase-shifted complex point source at the detected peak position is added to an empty spatial map and forms the \"complex clean map\". A \"complex residual map\" is also calculated by subtracting the complex dirty beam of this point source from the initial dirty map. Our algorithm repeats the same procedure, except the updated complex residual map is used instead of the complex dirty map to detect the power peak in consecutive iterations. Iteration continues until the peak power in the complex residual map falls below a desired level--for example, 30 dB below the peak power of the original complex dirty map.