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上海交通大学自然科学研究院最新成果:压缩感知图像处理中的局部-随机采样方法

近期,自然科学期刊Scientific Reports 发表了上海交通大学自然科学研究院及数学科学学院周栋焯蔡申瓯与Swarthmore College数学与统计学系Victor J. Barranca以及Rensselaer Polytechnic Institute数学系Gregor Kovacic合作完成的题为“Improved Compressive Sensing of Natural Scenes Using Localized Random Sampling”的论文(Sci. Rep. 6, 31976, 2016), 报道了他们关于自然图像处理的压缩感知理论中数据采样方法的最新进展。

压缩感知理论是近年来的一个热门领域,它被广泛用来处理类似自然图像这样的稀疏信号的存储与传输。在传统的压缩感知理论中,为了实现从低维测量输出来重构高维稀疏输入信号,测量信号时的数据采样方法通常是采用均匀-随机采样(uniformly-random sampling)方法,即数据采样矩阵中的不同行列的元素之间是相互独立的随机变量,我们基于生物视觉神经系统中神经元具有感受野概念的启发,提出了一种我们定义为局部-随机采样(localized-random sampling)的新的数据采样方法,即数据采样矩阵中的不同行列的元素之间不再是相互独立,而是具有一定关联性的随机变量,简单来说,采样矩阵每行元素离该行的采样点中心的距离越近,则被采样的概率越大。我们通过大量的图像算例系统比较了这两种采样方法在压缩感知重构图像时的效率,发现局部-随机采样方法要明显优于传统的均匀-随机采样方法,即针对相同数目的测量输出,利用局部-随机采样方法得到的重构图像的误差要明显低于传统的均匀-随机采样方法得到的重构图像的误差,进一步我们发现该优越性不依赖于压缩感知图像重构的算法和图像稀疏表示的方法,而且局部-随机采样方法中优化参数的选取也不依赖于自然图像的内容,具有很强的普适性,该方法为压缩感知理论在图像处理领域的应用提供了新的思路。

参考文献:Victor J. Barranca, Gregor Kovacic, Douglas Zhou, David Cai, “Improved Compressive Sensing of Natural Scenes Using Localized Random Sampling”, Scientific Reports, 6, 31976, 2016.

Compressive sensing (CS) theory demonstrates that by using uniformly-random sampling, rather than uniformly-spaced sampling, higher quality image reconstructions are often achievable. Considering that the structure of sampling protocols has such a profound impact on the quality of image reconstructions, we formulate a new sampling scheme motivated by physiological receptive field structure, localized random sampling, which yields significantly improved CS image reconstructions. For each set of localized image measurements, our sampling method first randomly selects an image pixel and then measures its nearby pixels with probability depending on their distance from the initially selected pixel. We compare the uniformly-random and localized random sampling methods over a large space of sampling parameters, and show that, for the optimal parameter choices, higher quality image reconstructions can be consistently obtained by using localized random sampling. In addition, we argue that the localized random CS optimal parameter choice is stable with respect to diverse natural images, and scales with the number of samples used for reconstruction. We expect that the localized random sampling protocol helps to explain the evolutionarily advantageous nature of receptive field structure in visual systems and suggests several future research areas in CS theory and its application to brain imaging.