A variational approach to waveform design for synthetic aperture imaging

Abstract. We derive an optimal transmit waveform for filtered backprojectionbased synthetic-aperture imaging. The waveform is optimal in terms of minimising the mean square error (MSE) in the resulting image. Our optimization is performed in two steps: First, we consider the minimum-mean-square-error (MMSE) for an arbitrary but fixed waveform, and derive the corresponding filter for the filtered backprojection reconstruction. Second, the MMSE is further reduced by finding an optimal transmit waveform. The transmit waveform is derived for stochastic models of the scattering objects of interest (targets), other scattering objects (clutter), and additive noise. We express the waveform in terms of spatial spectra for the random fields associated with target and clutter, and the spectrum for the noise process. This approach results in a constraint that involves only the amplitude of the Fourier transform of the transmit waveform. Therefore, considerable flexibility is left for incorporating additional requirements, such as minimal variation of transmit amplitude and phase-coding

Mating type idiomorphs of Pyrenophora teres in Turkey

Pyrenophora teres f. maculata (Ptm) and Pyrenophora teres f. teres (Ptt) causes spot form and net form of net blotch diseases of barley, respectively. Although both forms of P. teres are morphologically similar, their symptoms and genetic background differ. In this study, 175 single spore (109 Ptm and 66 Ptt) isolates obtained from different regions of Turkey were evaluated for their mating type distribution and prevalence. Fungal isolates of both forms were verified using species-speci.c polymerase chain reaction (PCR) primers. For mating type determination studies, duplex PCR was performed using MAT-specific single nucleotide polymorphism primers. Sixty and 49 of 109 Ptm isolates were found as MAT1-1 and MAT1-2 types, respectively and 43 and 23 of 66 Ptt isolates were found as MAT1-1 and MAT1-2 types, respectively. These results show the possibility of sexual reproduction among the Ptm isolates in Turkey and Ptt population of Central Anatolia, Turkey. However, the overall pattern of Ptt isolates did not support the sexual reproduction hypothesis in Turkey. Sexual reproduction in the life cycle of P. teres is important since it could lead to genetic and pathogenic variation. As a result of new sexual combinations more virulent pathotypes of P. teres may occur

Symbolic polynomial interpolation using Mathematica

This paper discusses teaching polynomial interpolation with the help of Mathematica. The symbolic power of Mathematica is utilized to prove a theorem for the error term in Lagrange interpolating formula. Derivation of the Lagrange formula is provided symbolically and numerically. Runge phenomenon is also illustrated. A simple and efficient symbolic derivation of cubic splines is also provided

2d polynomial interpolation: A symbolic approach with mathematica

This paper extends a previous work done by the same authors on teaching 1d polynomial interpolation using Mathematica [1] to higher dimensions. In this work, it is intended to simplify the the theoretical discussions in presenting multidimensional interpolation in a classroom environment by employing Mathematica's symbolic properties. In addition to symbolic derivations, some numerical tests are provided to show the interesting properties of the higher dimensional interpolation problem. Runge's phenomenon was displayed for 2d polynomial interpolation