论文标题
线性操作员通过产品卷积扩展的快速小波分解
Fast Wavelet Decomposition of Linear Operators through Product-Convolution Expansions
论文作者
论文摘要
整体操作员的小波分解已证明它们在减少许多问题的计算时间方面的效率，从波浪或流体的模拟到成像中反向问题的解决。不幸的是，计算分解本身就是一个严重的问题，对于大规模问题而言，这通常是遥不可及的。这项工作的目的是根据另一种称为产品卷积扩展的表示快速分解算法。可以有效地评估这种分解，假设可用的几个脉冲响应可用，但是在迭代方法中掺入时，通常比小波分解效率低。提出的分解算法在准线性时间内运行，我们提供了一些数值实验，以评估其在涉及空间变化的成像问题的性能。
Wavelet decompositions of integral operators have proven their efficiency in reducing computing times for many problems, ranging from the simulation of waves or fluids to the resolution of inverse problems in imaging. Unfortunately, computing the decomposition is itself a hard problem which is oftentimes out of reach for large scale problems. The objective of this work is to design fast decomposition algorithms based on another representation called product-convolution expansion. This decomposition can be evaluated efficiently assuming that a few impulse responses of the operator are available, but it is usually less efficient than the wavelet decomposition when incorporated in iterative methods. The proposed decomposition algorithms, run in quasi-linear time and we provide some numerical experiments to assess its performance for an imaging problem involving space varying blurs.
