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Reconstruction of complex signals using minimum Renyi information

机译:使用最少的仁义信息重建复杂信号

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Abstract: An information divergence, such as Shannon mutual information, measures the `distance' between two probability density functions (or images). A wide class of such measures, called $alpha@-divergences, with desirable properties such as convexity over all space, has been defined by Amari. Renyi's information D$-$alpha$/ is an $alpha@-divergence. Because of its convexity property, minimization of D$-$alpha$/ is easily attained. Minimization accomplishes minimum distance (maximum resemblance) between an unknown image and a known, reference image. Such a biasing effect permits complex images, such as occur in ISAR imaging, to be well reconstructed. There, the bias image may be constructed as a smooth version of the linear. Fourier reconstruction of the data. Examples on simulated complex image data, with and without noise, indicate that the Renyi reconstruction approach permits super-resolution in low-noise cases, and higher fidelity over ordinary, linear reconstructions in higher-noise cases. !15
机译:摘要:诸如Shannon互信息之类的信息散度测量两个概率密度函数(或图像)之间的“距离”。阿玛瑞(Amari)已定义了各种各样的此类度量,称为$ alpha @ -divergences,它们具有理想的属性,例如在所有空间上都具有凸度。 Renyi的信息D $-$ alpha $ /是一个$ alpha @-分歧。由于其凸性,可以轻松实现D $-$ alpha $ /的最小化。最小化可实现未知图像与已知参考图像之间的最小距离(最大相似度)。这样的偏置效果允许诸如ISAR成像中出现的复杂图像被很好地重建。在那里,偏置图像可以被构造为线性的平滑形式。数据的傅立叶重构。带有或不带有噪声的模拟复杂图像数据的示例表明,Renyi重建方法在低噪声情况下可以实现超分辨率,而在较高噪声情况下则可以实现比普通线性重建更高的保真度。 !15

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