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Appended the code in the question. Please have a look & feel free to give comments.

It works correctly with the simple matrix I posted above. Not sure if I apply it on image, but at least the program can run when I input an image & seems fine to me. I was unable to post the code at the moment, seems that new user in this website is only allowed to answer own question after 2 days of registration. Insufficient characters space to post in comment.

Your suggestion is a bit similar to my trial before, but that time I grabbed the complex channel first and do inverse together with real channel. Somehow, I couldn't get correct result, maybe due to errors in my program. However, I received a solution and I solved my problem now. I have to manipulate the complex matrix in a way to form a real matrix (1 channel) containing the real and imaginary parts of the complex matrix, as explained in http://home.earthlink.net/~w6rmk/math/matinv.htm Do the invert function, then arrange the real and imaginary results back to a 2-channel matrix again. Thanks a lot for your response anyway, as I am still fresh with OpenCV and programming. I am grateful with all the receiving responses.

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).

(Written in C++) Let's say I have a matrix 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);

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

OpenCV Error: Assertion failed (type == CV_32F || type == CV_64F) in invert

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.

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.

From the solution I received, it's something like this:

void invComplex(const cv::Mat& m, cv::Mat& inverse)

{ cv::Mat twiceM = cv::Mat(m.rows * 2, m.cols * 2,CV_64FC1);

std::vector<cv::Mat> comp;
cv::split(m,comp);

cv::Mat real = comp[0];
cv::Mat imag = comp[1];

for(int i=0; i<m.rows; i++)
{
    for(int j=0; j<m.cols; j++)
    {
        twiceM.at<double>(i,j) = real.at<double>(i,j);
        twiceM.at<double>(i,j + m.cols) = imag.at<double>(i,j);
        twiceM.at<double>(i + m.rows,j) = -imag.at<double>(i,j);
        twiceM.at<double>(i + m.rows,j + m.cols) = real.at<double>(i,j);
    }
}

cv::Mat twiceInv;
cv::invert(twiceM,twiceInv);

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

for(int i=0; i<inverse.rows; i++)
{
    for(int j=0; j<inverse.cols; j++)
    {
        double re = twiceInv.at<double>(i,j);
        double im = twiceInv.at<double>(i,j + inverse.cols);

        cv::Vec2d val(re,im);

        inverse.at<cv::Vec2d>(i,j) = val;
    }
}

}