Fractal-based methods in analysis and signal image processing

基于分形的近似方法利用被分析对象的数学自相似性。在数字信号/图像中发现这种自相似性有助于构建基于分形的图像操作算法，如压缩和去噪。例如，当图像通过计算机或移动电话连接传输时，这种操作是非常值得关注的。最近的一项进展涉及到通过基于分形的技术构建“轨道图像”。轨道图像的一个简单例子是一片玉米地或一片花消失在地平线上。除了允许这样的图像在计算机上以惊人的速度呈现之外，这些想法在图像表示方面还有其他应用。在实验观察到的数据中发现这种自相似性，可以使我们能够近似所研究现象的数学模型中的参数值。如果数学模型是未知的，我们也许能够确定它的形式。广泛领域的科学研究需要有效的模型识别和参数估计技术。

Fractal-based approximation methods take advantage of mathematical self-similarity in the object being analyzed. Finding such self-similarity in a digital signals/images facilitates the construction of fractal-based algorithms for image operations such as compression and denoising.  Such operations are of great concern when images are transmitted over a computer or cell phone connection, for example.  A very recent advancement involves the construction of "orbital pictures" via fractal-based techniques.  A simple example of an orbital picture is a field of corn or flowers disappearing off to the horizon.  Besides allowing for such images to be rendered with remarkable speed on a computer, there are other applications of these ideas to image representation. Finding such self-similarity in experimentally observed data can enable us to approximate the values of parameters in the mathematical model of the phenomenon being studied.  If the mathematical model is unknown, we may be able to determine its form.  Scientific research in a wide range of areas requires efficient model identification and parameter estimation techniques.