利用空间稀疏性实现多波长光学干涉成像
Exploiting spatial sparsity for multi-wavelength imaging in optical interferometry
摘要：
光学干涉仪提供多波长测量。为了充分利用这些仪器的光谱和空间分辨率，必须开发用于图像重建的新算法。处理多色干涉测量数据的早期尝试包括在某些光谱带宽中恢复物体的灰色图像或独立的单色图像。现在的主要挑战是恢复完整的三维（空间光谱）的亮度分布的天文目标给定的所有可用数据。我们描述了一种新的方法来实现多波长的图像重建的情况下，观察到的场景是一个点样源的集合。我们展示了通过全局考虑所有数据而不是处理独立的光谱切片来实现的图像质量（空间和光谱）的增益。这是通过正则化实现的，正则化有利于源的空间稀疏性和频谱分组。由于目标函数是不可微的，我们不得不开发一种专门的优化算法，该算法还考虑了亮度分布的非负性。
英文摘要：
Optical interferometers provide multiple wavelength measurements. In order to fully exploit the spectral and spatial resolution of these instruments, new algorithms for image reconstruction have to be developed. Early attempts to deal with multi-chromatic interferometric data have consisted in recovering a gray image of the object or independent monochromatic images in some spectral bandwidths. The main challenge is now to recover the full 3-D (spatio-spectral) brightness distribution of the astronomical target given all the available data. We describe a new approach to implement multi-wavelength image reconstruction in the case where the observed scene is a collection of point-like sources. We show the gain in image quality (both spatially and spectrally) achieved by globally taking into account all the data instead of dealing with independent spectral slices. This is achieved thanks to a regularization which favors spatial sparsity and spectral grouping of the sources. Since the objective function is not differentiable, we had to develop a specialized optimization algorithm which also accounts for non-negativity of the brightness distribution.
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