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Photoacoustic (PA) imaging - an emerging, noninvasive, biomedical imaging modality combining both optics and ultrasonic - allows in vivo visualization of embedded light absorbing structures.In this technique, a biological tissue sample is illuminated with short pulses of laser light at a wavelength typically in the red or near-infrared (NIR) region. The absorption of light causes local heating which produces pressure waves, known as PA waves, via thermoelastic expansion. By using a wideband ultrasonic transducer one can acquire the PA waves that propagate back to the tissue surface. A single-element ultrasonic transducer or a transducer array is used to obtain the PA waves at various locations around the surface of the tissue. These PA waves are then used to reconstruct the initial pressure rise. Initial pressure rise is proportional to the absorbed optical energy, whichis proportional to the light fluence distribution in the tissue and the absorption coefficient of the tissue. If a homogeneous fluence distribution is assumed then the initial pressure rise can be used to map the absorption coefficient of the tissue. Here, a k-wave MATLAB toolbox was used to simulate various configurations of excitation pulse shape, width, transducer types, and target object sizes to see their effect on the photoacoustic/ thermoacoustic signals. A numerical blood vessel phantom was also used to demonstrate the effect of various excitation pulse waveforms and pulse widths on the reconstructed images. Reconstructed images were blurred due to the broadening of the pressure waves by the excitation pulse width as well as by the limited transducer bandwidth. The blurring increases with increase in pulse width. A deconvolution approach with Tikhonov regularization to correct the photoacoustic/thermoacoustic signals, resulted in improved reconstructed images byreducing the blurring effect. It is observed that the reconstructed images remain unaffected by change in pulse widths or pulse shapes, as well as by the limited bandwidth of the ultrasound detectors after the use of the deconvolution technique.

Figure: (A) Numerical blood vessel network phantom. Initial pressure rise assumed to be 1 Pa. Reconstructed images using k-wave time reversal method for various excitation pulse widths (B) 0.25 s, (C) 0.5 s, (D) 1 s, and (E) 2 s. Excitation pulse is gaussian. (F-I) Corresponding reconstructed images after deconvolution operation.

The cost function can be modelled as

where R is the Regularization function. We want to explore different R by constructing an efficient optimization method. The computational efficiency of optimization method depends on how good we model H^{^}J where H^{^}J is the approximate Hessian matrix. Efficient modelling of H^{^}J will depend on how well we model H^TH. We are presently trying to build a computationally efficient space variant convolution model.