DOES THE MAXIMUM-ENTROPY METHOD IMPROVE SENSITIVITY
DOES THE MAXIMUM-ENTROPY METHOD IMPROVE SENSITIVITY
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DOI：
10.1073/pnas.87.13.5066
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发表时间：
1990-07-01
影响因子：
11.1
通讯作者：
HOCH, JC
中科院分区：
文献类型：
--
作者：
DONOHO, DL;JOHNSTONE, IM;HOCH, JC
最大熵重建已经在几个领域中使用，以从噪声、间接测量中产生阳性对象（图像、密度、光谱）的视觉上引人注目的重建。在磁共振波谱学中，该技术以其明显的噪声抑制和避免影响短（零扩展）数据记录的离散傅里叶变换谱的伪影而闻名。在重建光谱的长度超过数据记录的长度或者在重建中包含卷积核的一般情况下，不存在重建问题的已知解析解。因此，知识的最大熵重建的属性一直主要是轶事，基于一个小的选择出版的重建。然而，在有限的情况下，重建的光谱和数据记录的长度是相同的，卷积核不适用，这个问题可以解析地解决。该解决方案具有简单的结构，有助于解释最大熵重建的几个常见特征-例如，恢复强度的偏差以及基线附近的噪声比叠加在光谱中的广泛特征上的噪声更成功地抑制的事实。该解决方案还表明，由最大熵重建提供的噪声抑制可以（在这种特殊情况下）同样很好地通过“化妆品”设备获得：简单地显示传统的傅里叶变换重建，使用垂直（y）坐标的某个非线性绘图比例。
Maximum entropy reconstruction has been used in several fields to produce visually striking reconstructions of positive objects (images, densities, spectra) from noisy, indirect measurements. In magnetic resonance spectroscopy, this technique is notable for its apparent noise suppression and its avoidance of the artifacts that affect discrete Fourier transform spectra of short (zero-extended) data records. In the general case where the length of the reconstructed spectrum exceeds that of the data record or where a convolution kernel is incorporated in the reconstruction, no known analytical solution to the reconstruction problem exists. Consequently, knowledge of the properties of maximum entropy reconstruction has been mainly anecdotal, based on a small selection of published reconstructions. However, in the limiting case where the lengths of the reconstructed spectrum and the data record are the same and a convolution kernel is not applied, the problem can be solved analytically. The solution has a simple structure that helps explain several commonly observed features of maximum entropy reconstructions--for example, the biases in the recovered intensities and the fact that noise near the baseline is more successfully suppressed than is noise superimposed on broad features in the spectrum. The solution also shows that the noise suppression offered by maximum entropy reconstruction could (in this special case) be equally well obtained by a "cosmetic" device: simply displaying the conventional Fourier transform reconstruction using a certain nonlinear plotting scale for the vertical (y) coordinate.