How can I remove the central pattern (near 0 hz value) correctly?

I want to perform a 2D Fast Fourier Transform on a matrix (named hstg, attached to this question) and observe its behavior around 0 frequency.

The size of the matrix hstg is 1024*1024, before processing, I applied a window function to this matrix.

windowf = hann(1024)*hann(1024)';
hstg = hstg.*windowf;

sq = fft2(hstg);
sq1 = (abs(fftshift(sq)));

imagesc(-sq1);
clim([-15 0]);

As the picture shows, there is a large range of abnormally large intensity in the center, which is near the 0 frequency.

To solve this problem, I used the method of subtracting the mean.

While keeping the window function type still, I applied

hstg = (hstg - mean2(hstg.*windowf)/mean2(windowf)).*windowf;

It worked but failed to satisfy me.

Then I tried a high pass filter.

cutOffFrequency = 0.005;
filterOrder = 3;
filteredRows = zeros(size(hstg));
for i = 1:size(hstg, 1)
    filteredRows(i, :) = highpass(hstg(i, :), cutOffFrequency, filterOrder);
end
filteredMatrix = zeros(size(hstg));
for j = 1:size(hstg, 2)
    filteredMatrix(:, j) = highpass(filteredRows(:, j), cutOffFrequency, filterOrder);
end
hstg = filteredMatrix;

I'm afraid that I might do it wrong, 'cause judging from the result, the intensity of the central part is simply deleted.

So I sincerely hope that someone can give me some suggestions to solve this problem.

I will check carefully any answer, and the matrix hstg is attached to this question.

Answer 1

[Image Analyst]

It looks like it's deleting the spectrum along the axes. If you just want the central spot, then just erase that:

[rows, columns] = size(sq1);
midRow = floor(rows/2)
midCol = floor(columns/2)
windowWidth = 5; % Whatever you want to erase.
sq1(midRow - windowWidth : midRow + windowWidth, midCol - windowWidth : midCol + windowWidth) = 0;

See attached demos using demo image, not yours.