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New adaptive and progressive image transmission approach using function superpositions

机译：使用函数叠加的新型自适应渐进图像传输方法

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摘要

We present a novel approach to adaptive and progressive image transmission, based on the decomposition of an image into compositions and superpositions of monovariate functions. The monovariate functions are iteratively constructed and transmitted, one after the other, to progressively reconstruct the original image: the progressive transmission is performed directly in the 1D space of the monovariate functions and independently of any statistical properties of the image. Each monovariate function contains only a fraction of the pixels of the image. Each new transmitted monovariate function adds data to the previously transmitted monovariate functions. After each transmission step, by using the updated monovariate functions the image is reconstructed with an increased resolution. Finally, once all the monovariate functions have been transmitted, the original image is reconstructed exactly. This approach is characterized by its flexibility and robustness to packet loss: any numbers of intermediate transmissions and reconstructions are possible, and in case of packet loss, the global appearance of the transmitted image is preserved. Moreover, the intermediate images can be reconstructed at any resolution, and for any number of intermediate reconstructions, the original image will be exactly reconstructed. Finally, the quantity of data to be transmitted only depends on the image size and is independent of the number of intermediate reconstructions. Our main contributions are the modification of the decomposition scheme defined by the Kolmog-orov superposition theorem to enable multiresolution image reconstructions and its application for progressive image transmission, using successively increasing resolutions. We illustrate this approach on several images and evaluate the reconstruction quality, decomposition flexibility, and error resilience during transmission.
机译：我们基于将图像分解为单变量函数的组成和叠加，提出了一种自适应和渐进式图像传输的新颖方法。单变量函数以迭代的方式构造和传输，以逐步重建原始图像：逐行传递直接在单变量函数的一维空间中执行，并且与图像的任何统计属性无关。每个单变量函数仅包含图像像素的一小部分。每个新发送的单变量函数将数据添加到先前发送的单变量函数。在每个传输步骤之后，通过使用更新的单变量函数，可以以更高的分辨率重建图像。最后，一旦所有单变量函数都已发送，原始图像将被精确重建。这种方法的特点是它对数据包丢失的灵活性和鲁棒性：任何数量的中间传输和重构都是可能的，并且在数据包丢失的情况下，可以保留传输图像的整体外观。而且，可以以任何分辨率重建中间图像，并且对于任何数量的中间重建，原始图像将被精确地重建。最后，要传输的数据量仅取决于图像大小，并且与中间重建的数量无关。我们的主要贡献是对由Kolmog-orov叠加定理定义的分解方案的修改，以实现多分辨率图像重建及其在逐级图像传输中的应用，并使用逐级提高的分辨率。我们在几张图像上说明了这种方法，并评估了传输过程中的重建质量，分解灵活性和错误恢复能力。

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