如何在OpenCV中对复杂矩阵求逆?

问题描述

我在做一个复杂矩阵的逆时遇到麻烦.据我所知，复数矩阵只是一个两通道矩阵(CV_32FC2/CV_64FC2).

I have trouble in doing inverse of a complex matrix. As far as I know, complex matrix is simply a two-channel matrix (CV_32FC2 / CV_64FC2).

假设我有一个矩阵C:

Mat C(2, 2, CV_64FC2);

C.at<Vec2d>(0,0)[0] = 1;
C.at<Vec2d>(0,0)[1] = 1;
C.at<Vec2d>(0,1)[0] = 3;
C.at<Vec2d>(0,1)[1] = 4;
C.at<Vec2d>(1,0)[0] = 2;
C.at<Vec2d>(1,0)[1] = -1;
C.at<Vec2d>(1,1)[0] = 5;
C.at<Vec2d>(1,1)[1] = 2;

Mat InverseMat;
invert(C, InverseMat, DECOMP_SVD);

执行反转功能后，我不断收到此错误:

After I perform the invert function, I keep getting this error:

invert函数可以很好地处理灰度加载的图像(1通道)，但是我很难对包含实部和虚部的复杂矩阵进行逆运算.

The invert function works well with a grayscale loaded image (1 channel), but I have hard time to do inverse on complex matrix which contains real and imaginary part.

有人可以告诉我如何解决复杂矩阵的逆问题吗?最好使用DECOMP_SVD方法，因为尝试单通道图像时由于使用DECOMP_LU或DECOMP_CHOLESKY方法无法获得理想的结果，可能是由于奇异矩阵的问题.谢谢.

Can someone please tell me how to solve the inverse problem of a complex matrix? Preferably using DECOMP_SVD method, as I can't get desired result using DECOMP_LU or DECOMP_CHOLESKY method when I tried with a single channel image, probably because of the matter of singular matrix. Thanks.

推荐答案

OpenCV不支持复杂矩阵的求逆.您必须以某种方式操纵复杂矩阵，以形成包含复杂矩阵的实部和虚部的实数矩阵. 此页面说明了该过程.

OpenCV does not support inversion of complex matrices. You have to manipulate the complex matrix in a way to form a real matrix containing the real and imaginary parts of the complex matrix. This page explains the process.

以下是使用上述过程对复杂矩阵求逆的代码:

Here is the code to perform inverse of a complex matrix using the above mentioned process:

//Perform inverse of complex matrix.
cv::Mat invComplex(const cv::Mat& m)
{
    //Create matrix with twice the dimensions of original
    cv::Mat twiceM(m.rows * 2, m.cols * 2, CV_MAKE_TYPE(m.type(), 1));

    //Separate real & imaginary parts
    std::vector<cv::Mat> components;
    cv::split(m, components);

    cv::Mat real = components[0], imag = components[1];

    //Copy values in quadrants of large matrix
    real.copyTo(twiceM({ 0, 0, m.cols, m.rows })); //top-left
    real.copyTo(twiceM({ m.cols, m.rows, m.cols, m.rows })); //bottom-right
    imag.copyTo(twiceM({ m.cols, 0, m.cols, m.rows })); //top-right
    cv::Mat(-imag).copyTo(twiceM({ 0, m.rows, m.cols, m.rows })); //bottom-left

    //Invert the large matrix
    cv::Mat twiceInverse = twiceM.inv();

    cv::Mat inverse(m.cols, m.rows, m.type());

    //Copy back real & imaginary parts
    twiceInverse({ 0, 0, inverse.cols, inverse.rows }).copyTo(real);
    twiceInverse({ inverse.cols, 0, inverse.cols, inverse.rows }).copyTo(imag);

    //Merge real & imaginary parts into complex inverse matrix
    cv::merge(components, inverse);
    return inverse;
}

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