Imaging beyond aliasing

A proper spatial sampling is critical for high quality imaging. If the sampling criterion is not met, artifacts appear in the image, generally referred to as grating lobes. For inspection efficiency the width of the field of view is becoming larger leading to an increase in the number of elements and therefore transducer complexity and cost. The development of volume scanning methods in the medical field poses its own problems. Here a matrix of piezoelements is used to scan a volume using electronic beam steering. The challenge is to connect 2500+ elements using <256 channels. Most solutions use prebeamforming to reduce the data at a cost of image quality. Another option may be to reconstruct the non-aliased data from spatially aliased data. In this work a novel method to reconstruct nonaliased radio-frequency (RF) data from strongly spatially aliased RF data is investigated using simulations and experiments. The reconstruction method involves an iterative scheme using wave field extrapolation. No medium assumptions are made. It has the following steps: 1) A matrix containing zeros at the locations where signals need to be interpolated is created such that no aliasing occurs. 2) The dataset is inversely extrapolated to focus the wave energy. 3) A threshold is applied to the extrapolated data selecting such that aliasing artifacts are excluded. 4) The dataset is forward extrapolated such that the input data is obtained. Now the empty traces contain signal. 6) The original RF dataset is copied into the reconstructed dataset. 7) Steps 2 - 6 are performed iteratively using a progressively lower threshold. Aliased and non-aliased datasets were modeled based on point diffractors and reflectors of increasing width. The datasets were imaged using a wavenumber-frequency domain mapping. The error after reconstruction was 0.77%, 4.2% and 43%, for undersampling of a factor 2, 4 and 8, respectively. For point diffractors the reconstruction error was 0.32%, 3.3% and 7.2%, respectively. These results show the method's potential. It may also be used to reconstruct signals for dead array elements.