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We obtain new relations involving the Lerch transcendent and establish some closed-form expressions using special functions like the Riemann and Hurwitz zeta functions and fractional sums. We also get some formulae for the specific values of the derivative of Lerch transcendent. Publisher's Version

We derived analytical forward and inverse solution of thermoacoustic wave equation for nonhomogeneous medium. We modelled the nonhomogeneous medium as a multi-layer planar medium and defined initial conditions, continuity conditions on the layer boundaries and radiation conditions at infinity assuming the source distribution existing in all layers. These solutions of thermoacoustic wave equation are based on the method of Green’s functions for layered planar media. For qualitative testing and comparison of the point-spread functions associated with the homogeneous and layered solutions, we performed numerical simulations. Our simulation results showed that the conventional inverse solution based on homogeneous medium assumption, as expected, produced incorrect locations of point sources, whereas our inverse solution involving the multi-layer planar medium produced point sources at the correct source locations. Also, we examined whether the performance of our layered inverse solution is sensitive to medium parameters used as priority information in the measured data. Our inverse solutions based on multi-layer planar media are applicable for cross-sectional two-dimensional imaging of abdominal structure and the organs such as breast and skin. This work was supported by TUBITAK of Turkey through ARDEB-1003 Program under Grant 213E038. We are immensely grateful to Prof. Dr. Mustafa Karaman who provided insight and expertise that assisted the research. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations Publisher's Version

For cross-sectional two-dimensional thermoacustic imaging of breast and brain, we explored solution of the wave equation using layered tissue model consisting of concentric annular layers on a cylindrical cross-section. To obtain the forward and inverse solutions of the thermoacoustic wave equation, we derived the Green's function involving Bessel and Hankel functions by employing the geometrical and acoustic parameters (densities and velocities) of layered media together with temporal initial condition, radiation conditions and continuity conditions on the layers' boundaries. The image reconstruction based on this approach involves the layer parameters as the apriori information which can be estimated from the acquired thermoacoustic data. To test and compare our layered solution with conventional solution based on homogeneous medium assumption, we performed simulations using numerical test phantoms consisting of sources distributed in the layered structure. This work was supported by TUBITAK of Turkey through ARDEB-1003 Program under Grant 213E038 Publisher's Version

25th Signal Processing and Communications Applications Conference (SIU) -- MAY 15-18, 2017 -- Antalya, TURKEY WOS: 000413813100597 Thermoacoustic imaging is a new modality of generating ultrasonic waves with excitation of electromagnetic pulsed energy. Thermoacoustic imaging is based on the inverse soluion of thermoacoustic wave equation. Homogeneous assumption of tissue to be imaged results in degradation of image qualtiy. In this study, we obtain an analytical inverse solution of thermoacoustic wave equation for 3-dimensional concentric cylindrical multi layer structures. This solution can be applied for imaging of breast and brain. To test our solution, we use a 3-layer test phantom consisting of point sources in numerical simulations. Turk Telekom, Arcelik A S, Aselsan, ARGENIT, HAVELSAN, NETAS, Adresgezgini, IEEE Turkey Sect, AVCR Informat Technologies, Cisco, i2i Syst, Integrated Syst & Syst Design, ENOVAS, FiGES Engn, MS Spektral, Istanbul Teknik Univ

25th Signal Processing and Communications Applications Conference (SIU) -- MAY 15-18, 2017 -- Antalya, TURKEY WOS: 000413813100593 In this study, we derive analytical forward and inverse solution of thermoacoustic wave equation for inhomogeneous multi-layer planar medium, where the source distribution can exist in all layers with different acoustic parameters. Our solutions are based on methods of the Greens functions for layered planar media. This model is applicable for imaging of tissue structures such as skin, breast and abdominal imaging. We have tested and compared our layered solution and conventional solution for point sources located in a two-layer by using numerical simulations. Turk Telekom, Arcelik A S, Aselsan, ARGENIT, HAVELSAN, NETAS, Adresgezgini, IEEE Turkey Sect, AVCR Informat Technologies, Cisco, i2i Syst, Integrated Syst & Syst Design, ENOVAS, FiGES Engn, MS Spektral, Istanbul Teknik Univ

We derived analytical forward and inverse solution of thermoacoustic wave equation for inhomogeneous multi layered planar and cylindrical mediums with the source distribution existing in all layers. These solutions are applicable for imaging of organs such as breast and brain, whose structures are suitable for multi-layer modelling. For qualitative testing and comparison of the point-spread-functions associated with the homogeneous and layered solutions, we performed numerical simulations. Our simulation results show that the conventional inverse solution based on homogeneous medium assumption, as expected, produces incorrect locations of point sources and significantly increased side lobes, whereas our inverse solution involving the multi-layered medium produces point sources at the correct locations with lower side lobes. This work was supported by TUBITAK of Turkey through ARDEB-1003 Program under Grant 213E038 Publisher's Version

By using the existence of a larger orthonormal basis, the space of strong limit power functions is extended. We use the windowed Fourier transform and wavelet transform to analyze strong limit power signals and we construct generalized frame decompositions using the discretized versions of these transforms. Publisher's Version Author Post Print

The main objective of this paper is to study the Hankel, fractional Hankel, and Bessel wavelet transforms using the Parseval relation. We construct a generalized frame and write new relations and inequalities using almost periodic functions, strong limit power signals, and these transform methods. Publisher's Version