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In this paper, regression function estimation from independent and
identically distributed data is considered. We establish strong
pointwise consistency of the famous Nadaraya-Watson estimator under weaker
conditions which permit to apply kernels with unbounded support and even not
integrable ones and provide a general approach for constructing strongly
consistent kernel estimates of regression functions.
Most existing reconstruction algorithms for photoacoustic
imaging (PAI) assume that transducers used to receive ultrasound signals
have infinite bandwidth. When transducers with finite bandwidth are used, this assumption
may result in reduction of the imaging contrast and distortions of reconstructed
images. In this paper, we propose a novel method to compensate the finite bandwidth
effect in PAI by using an optimal filter in the Fourier domain. Simulation results
demonstrate that the use of this method can improve the contrast of the reconstructed
images with finite-bandwidth ultrasound transducers.