奇怪的但是在c中关闭fft和ifft的图像

2023年10月8日 176次阅读

我编写了一个程序,可以在黑白png图像上加载,保存和执行fft和ifft.经过多次调试后头疼,我终于得到了一些连贯的输出,却发现它扭曲了原始图像.

输入：

FFT：

IFFT：

据我测试,每个阵列中的像素数据都被正确存储和转换.像素存储在两个数组中,’data’包含每个像素的b / w值,’complex_data’是’data’的两倍,并且在交替索引中存储每个像素的实际b / w值和虚部.我的fft算法在类似’complex_data’的数组上运行.在从用户读取命令的代码之后,这里是有问题的代码：

if (cmd == "fft")
        {              
            if (height > width) size = height;
            else size = width;

            N = (int)pow(2.0, ceil(log((double)size)/log(2.0)));

            temp_data = (double*) malloc(sizeof(double) * width * 2); //array to hold each row of the image for processing in FFT()

            for (i = 0; i < (int) height; i++)
            {
                for (j = 0; j < (int) width; j++)
                {
                    temp_data[j*2] = complex_data[(i*width*2)+(j*2)];
                    temp_data[j*2+1] = complex_data[(i*width*2)+(j*2)+1];
                }
                FFT(temp_data, N, 1);
                for (j = 0; j < (int) width; j++)
                {
                    complex_data[(i*width*2)+(j*2)] = temp_data[j*2];
                    complex_data[(i*width*2)+(j*2)+1] = temp_data[j*2+1];
                }
            }
            transpose(complex_data, width, height); //tested
            free(temp_data);
            temp_data = (double*) malloc(sizeof(double) * height * 2);
            for (i = 0; i < (int) width; i++)
            {
                for (j = 0; j < (int) height; j++)
                {
                    temp_data[j*2] = complex_data[(i*height*2)+(j*2)];
                    temp_data[j*2+1] = complex_data[(i*height*2)+(j*2)+1];
                }
                FFT(temp_data, N, 1);
                for (j = 0; j < (int) height; j++)
                {
                    complex_data[(i*height*2)+(j*2)] = temp_data[j*2];
                    complex_data[(i*height*2)+(j*2)+1] = temp_data[j*2+1];
                }
            }
            transpose(complex_data, height, width);

            free(temp_data);
            free(data);

            data = complex_to_real(complex_data, image.size()/4); //tested
            image = bw_data_to_vector(data, image.size()/4); //tested
            cout << "*** fft success ***" << endl << endl;



void FFT(double* data, unsigned long nn, int f_or_b){ // f_or_b is 1 for fft, -1 for ifft

unsigned long n, mmax, m, j, istep, i;
double wtemp, w_real, wp_real, wp_imaginary, w_imaginary, theta;
double temp_real, temp_imaginary;

// reverse-binary reindexing to separate even and odd indices
// and to allow us to compute the FFT in place

n = nn<<1;
j = 1;
for (i = 1; i < n; i += 2) {
    if (j > i) {
        swap(data[j-1], data[i-1]);
        swap(data[j], data[i]);
    }
    m = nn;
    while (m >= 2 && j > m) {
        j -= m;
        m >>= 1;
    }
    j += m;
};

// here begins the Danielson-Lanczos section

mmax = 2;
while (n > mmax) {
    istep = mmax<<1;
    theta = f_or_b * (2 * M_PI/mmax);
    wtemp = sin(0.5 * theta);
    wp_real = -2.0 * wtemp * wtemp;
    wp_imaginary = sin(theta);
    w_real = 1.0;
    w_imaginary = 0.0;
    for (m = 1; m < mmax; m += 2) {
        for (i = m; i <= n; i += istep) {
            j = i + mmax;
            temp_real = w_real * data[j-1] - w_imaginary * data[j];
            temp_imaginary = w_real * data[j] + w_imaginary * data[j-1];

            data[j-1] = data[i-1] - temp_real;
            data[j] = data[i] - temp_imaginary;
            data[i-1] += temp_real;
            data[i] += temp_imaginary;
        }
        wtemp = w_real;
        w_real += w_real * wp_real - w_imaginary * wp_imaginary;
        w_imaginary += w_imaginary * wp_real + wtemp * wp_imaginary;
    }
    mmax=istep;
}}

我的ifft只有在f_or_b设置为-1而不是1时才相同.我的程序在每一行调用FFT(),转换图像,再次调用每行上的FFT(),然后转置回来.我的索引可能有错误吗？

最佳答案 谢谢大家的意见.关于内存损坏的所有内容,虽然它是重点,但不是问题的根源.我正在使用的数据大小并不过大,我可以在正确的位置释放它们.在学习c时,我有很多练习.问题不在于fft算法,甚至也不是我的2D实现.

我错过的只是在我的ifft代码的末尾按1 /(M * N)缩放.因为图像是512×512,我需要将我的ifft输出缩放1 /(512 * 512).此外,我的fft看起来像白噪声,因为像素数据没有重新调整以适应0到255之间.

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