Ultrasound image reconstruction using the finite-rate-of-innovation principle

Recently, a method of finding the spectral samples of non-periodic-finite-rate-of-innovation (NP-FRI) signals using a sum-of-sincs (SoS) sampling kernel was proposed in the literature. In the SoS approach, the kernel is repeated at a rate dependent on the delays of the FRI signal. The number of repetitions depends on both the duration and the delays of pulses constituting the FRI signal. In this paper, we show that the kernel repetition can be avoided and perfect reconstruction can be obtained by working with the SoS kernel directly provided that certain sampling criteria are satisfied. We place a lower bound on the sampling rate to ensure that exact signal reconstruction is achieved using filtered samples. To suppress the effect of noise, we use Cadzow denoising technique. Reconstruction is achieved using the annihilating filter method. We report results on data simulated using Field II software as well as real cardiac ultrasound data. The experimental results show that, with nearly 10 times less data than that required by the standard technique, the proposed method gives a comparable quality of reconstruction. The reconstruction accuracy can be controlled by choosing the model order of the NP-FRI signal appropriately.