学习无乘法线性变换
Learning Multiplication-free Linear Transformations
AI总结：
本文提出了一种字典学习算法，用于稀疏表示，同时对学习到的字典施加特定结构，使其在数值上更高效：减少加法/乘法次数甚至避免乘法。我们基于字典的高结构化基本构建块（二进制正交、缩放和剪切变换）来建立工作，可以写出优化问题的闭式解。我们在图像数据上展示了方法的有效性，并与已知的数值高效变换如快速傅里叶变换和快速离散余弦变换进行比较。
摘要：
在本文中，我们提出了几种字典学习算法，用于稀疏表示，同时对学习到的字典施加特定结构，使得它们在数值上更高效：减少加法/乘法的次数，甚至避免乘法。我们的工作基于字典的高结构化基本构建块（二进制正交、缩放和剪切变换）来建立，可以写出我们考虑的优化问题的闭式解。我们在图像数据上展示了我们方法的有效性，并可以与已知的数值高效变换如快速傅里叶变换和快速离散余弦变换进行比较。
英文摘要：
In this paper, we propose several dictionary learning algorithms for sparse representations that also impose specific structures on the learned dictionaries such that they are numerically efficient to use: reduced number of addition/multiplications and even avoiding multiplications altogether. We base our work on factorizations of the dictionary in highly structured basic building blocks (binary orthonormal, scaling and shear transformations) for which we can write closed-form solutions to the optimization problems that we consider. We show the effectiveness of our methods on image data where we can compare against well-known numerically efficient transforms such as the fast Fourier and the fast discrete cosine transforms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
