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Yayın A factorized high dimensional model representation on the nodes of a finite hyperprismatic regular grid(Elsevier Science inc, 2005-05-25) Tunga, Mehmet Alper; Demiralp, MetinWhen the values of a multivariate function f(x(1),...,x(N)), having N independent variables like x(1),...,x(N) are given at the nodes of a cartesian, product set in the space of the independent variables and ail interpolation problem is defined to find out the analytical structure of this function some difficulties arise in the standard methods due to the multidimensionality of the problem. Here, the main purpose is to partition this multivariate data into low-variate data and to obtain the analytical structure of the multivariate function by using this partitioned data. High dimensional model representation (HDMR) is used for these types of problems. However, if HDMR requires all components, which means 2(N) number of components, to get a desired accuracy then factorized high dimensional model representation (FHDMR) can be used. This method uses the components of HDMR. This representation is needed when the sought multivariate function has a multiplicative nature. In this work we introduce how to utilize FHDMR for these problems and present illustrative examples.Yayın Hybrid high dimensional model representation (HHDMR) on the partitioned data(Elsevier B.V., 2006-01-01) Tunga, Mehmet Alper; Demiralp, MetinA multivariate interpolation problem is generally constructed for appropriate determination of a multivariate function whose values are given at a finite number of nodes of a multivariate grid. One way to construct the solution of this problem is to partition the given multivariate data into low-variate data. High dimensional model representation (HDMR) and generalized high dimensional model representation (GHDMR) methods are used to make this partitioning. Using the components of the HDMR or the GHDMR expansions the multivariate data can be partitioned. When a cartesian product set in the space of the independent variables is given, the HDMR expansion is used. On the other band, if the nodes are the elements of a random discrete data the GHDMR expansion is used instead of HDMR. These two expansions work well for the multivariate data that have the additive nature. If the data have multiplicative nature then factorized high dimensional model representation (FHDMR) is used. But in most cases the nature of the given multivariate data and the sought multivariate function have neither additive nor multiplicative nature. They have a hybrid nature. So, a new method is developed to obtain better results and it is called hybrid high dimensional model representation (HHDMR). This new expansion includes both the HDMR (or GHDMR) and the FHDMR expansions through a hybridity parameter. In this work, the general structure of this hybrid expansion is given. It has tried to obtain the best value for the hybridity parameter. According to this value the analytical structure of the sought multivariate function can be determined via HHDMR.Yayın Coherent array imaging using phased subarrays. Part II: Simulations and experimental results(IEEE-INST Electrical Electronics Engineers Inc, 2005-01) Johnson, Jeremy A.; Oralkan, Ömer; Ergün, Arif Sanlı; Demirci, Utkan; Karaman, Mustafa; Khuri-Yakub, Butrus ThomasThe basic principles and theory of phased subarray (PSA) imaging imaging provides the flexibility of reducing I he number of front-end hardware channels between that of classical synthetic aperture (CSA) imaging-which uses only one element per firing event-and full-phased array (FPA,) imaging-which uses all elements for each firing. The performance of PSA generally ranges between that obtained by CSA and FPA using the same array, and depends on the amount of hardware complexity reduction. For the work described in this paper, we performed FPA, CSA, and PSA imaging of a resolution phantom using both simulated and experimental data from a 3-MHz, 3.2-cm, 128-element capacitive micromachined ultrasound transducer (CMUT) array. The simulated system point responses in the spatial and frequency domains are presented as a means of studying the effects of signal bandwidth, reconstruction filter size, and subsampling rate on the PSA system performance. The PSA and FPA sector-scanned images were reconstructed using the wideband experimental data with 80% fractional bandwidth, with seven 32-element subarrays used for PSA imaging. The measurements on the experimental sector images indicate that, at the transmit focal zone, the PSA method provides a 10% improvement in the 6-dB lateral resolution, and the axial point resolution of PSA imaging is identical to that of FPA imaging. The signal-to-noise ratio (SNR) of PSA image was 58.3 dB, 4.9 dB below that of the FPA image, and the contrast-to-noise ratio (CNR) is reduced by 10%. The simulated and experimental test results presented in this paper validate theoretical expectations and illustrate the flexibility of PSA imaging as a way to exchange SNR and frame rate for simplified front-end hardware.












