Fast algorithm for least-squares based image prediction

Andrew Martchenko; Guang Deng

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Fast algorithm for least-squares based image prediction

机译：基于最小二乘的图像预测快速算法

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A new computationally efficient algorithm for two-dimensional sliding-window least-squares prediction is presented in this study. The fast algorithm is based on a recursive update of the Cholesky decomposition. Compared with the state-of-the-art algorithm, the proposed algorithm reduces the computational complexity from O(D3) to O(D2h), where D is the predictor order and h is the height of the prediction patch. The computational improvement is made at the stage of solving the normal equations for which an update algorithm for the Cholesky decomposition of the covariance matrix is proposed. It is shown that a large part of the Cholesky decomposition at location n can be efficiently calculated by performing orthonormal updates on the Cholesky decomposition at n - 1. The computational improvement is made without requiring additional storage space. Extensive experiments using causal and non-causal predictors of varying shapes and sizes have confirmed that the proposed algorithm is consistently faster than the state-of-the-art algorithm and produces identical prediction images. The efficiency of the proposed algorithm is shown to be affected by the order in which pixels are sampled, thus an ordering procedure is proposed to minimise the number of numerical operations.

机译：提出了一种新的计算有效的二维滑窗最小二乘预测算法。快速算法基于Cholesky分解的递归更新。与最新算法相比，该算法将计算复杂度从O（D3）降低到O（D2h），其中D是预测变量的阶数，h是预测补丁的高度。在求解正规方程的阶段进行了计算改进，为此提出了一种用于协方差矩阵的Cholesky分解的更新算法。结果表明，通过对n-1处的Cholesky分解执行正交更新，可以有效地计算出位置n处的大部分Cholesky分解。无需额外的存储空间即可进行计算改进。使用各种形状和大小的因果和非因果预测因子进行的广泛实验已证实，所提出的算法始终比最新算法更快，并且产生相同的预测图像。所提出算法的效率被显示为受到像素采样顺序的影响，因此提出了一种排序程序以最小化数值运算的数量。

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《Image Processing, IET》 |2016年第8期|582-589|共8页
作者
Andrew Martchenko; Guang Deng;
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La Trobe University, Australia;

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机译： src =“ / images / tex / 28215.gif” alt =“ ell _ {scriptscriptstyle 0}”> -正规化最小二乘的基于同伦算法
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机译：基于总最小二乘和近邻分裂的摄动压缩感知快速重建算法
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机译：基于指数加权最小二乘误差的快速自适应滤波算法
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机译：快速时变信道上OFDM通信的基于特征值分解的递归最小二乘算法
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机译：多维线性最小二乘问题的快速算法
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机译：使用最小二乘准则和算法进行快速约会
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机译：多维随机场线性最小二乘估计的快速算法。

Fast algorithm for least-squares based image prediction

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