IEEE Trans Image Process. 2015 Nov;24(11):4540-55. doi: 10.1109/TIP.2015.2463084. Epub 2015 Jul 30.
Even though image signals are typically defined on a regular 2D grid, there also exist many scenarios where this is not the case and the amplitude of the image signal only is available for a non-regular subset of pixel positions. In such a case, a resampling of the image to a regular grid has to be carried out. This is necessary since almost all algorithms and technologies for processing, transmitting or displaying image signals rely on the samples being available on a regular grid. Thus, it is of great importance to reconstruct the image on this regular grid, so that the reconstruction comes closest to the case that the signal has been originally acquired on the regular grid. In this paper, Frequency Selective Reconstruction is introduced for solving this challenging task. This algorithm reconstructs image signals by exploiting the property that small areas of images can be represented sparsely in the Fourier domain. By further considering the basic properties of the optical transfer function of imaging systems, a sparse model of the signal is iteratively generated. In doing so, the proposed algorithm is able to achieve a very high reconstruction quality, in terms of peak signal-to-noise ratio (PSNR) and structural similarity measure as well as in terms of visual quality. The simulation results show that the proposed algorithm is able to outperform state-of-the-art reconstruction algorithms and gains of more than 1 dB PSNR are possible.
尽管图像信号通常在规则的 2D 网格上定义，但也存在许多情况并非如此，并且仅可获取图像信号的非规则子集的像素位置的幅度。在这种情况下，必须对图像进行规则网格的重采样。由于处理、传输或显示图像信号的几乎所有算法和技术都依赖于规则网格上可用的样本，因此这是必要的。因此，在这个规则的网格上重建图像非常重要，以便重建最接近信号最初在规则网格上获取的情况。在本文中，引入了频率选择重建来解决这个具有挑战性的任务。该算法通过利用图像的小区域可以在傅立叶域中稀疏表示的特性来重建图像信号。通过进一步考虑成像系统的光学传递函数的基本特性，迭代地生成信号的稀疏模型。通过这样做，所提出的算法能够实现非常高的重建质量，在峰值信噪比 (PSNR) 和结构相似性度量以及视觉质量方面。模拟结果表明，所提出的算法能够优于最先进的重建算法，并且可以获得超过 1dB PSNR 的增益。
