FFT.inl

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/*

Copyright (c) 2016-2023, Dr Franck P. Vidal, Bangor University, All rights reserved.
Copyright (c) 2023-present, Prof Franck P. Vidal (franck.vidal@stfc.ac.uk), 
UK Research and Innovation, All rights reserved.


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//******************************************************************************
//  Define
//******************************************************************************


//******************************************************************************
//  Include
//******************************************************************************
#include <cmath>
#include <complex>

#ifdef HAS_FFTW
#include <fftw3.h>
#endif

#ifndef __Exception_h
#include "Exception.h"
#endif


//******************************************************************************
//  namespace
//******************************************************************************
namespace gVirtualXRay {


//---------------------------------
template<typename T> FFT<T>::FFT():
//---------------------------------
    m_origin_image_width(0),
    m_origin_image_height(0)
//---------------------------------
{}


//---------------------------------------------------
template<typename T> FFT<T>::FFT(const FFT<T>& aFFT):
//---------------------------------------------------
    m_real(aFFT.m_real),
    m_img(aFFT.m_img),
    m_origin_image_width(aFFT.m_origin_image_width),
    m_origin_image_height(aFFT.m_origin_image_height)
//---------------------------------------------------
{}


//----------------------------------------------------------------
template<typename T> FFT<T>& FFT<T>::operator=(const FFT<T>& aFFT)
//----------------------------------------------------------------
{
    m_real                = aFFT.m_real;
    m_img                 = aFFT.m_img;
    m_origin_image_width  = aFFT.m_origin_image_width;
    m_origin_image_height = aFFT.m_origin_image_height;

    return (*this);
}


//---------------------------------------------------------------------
template<typename T> FFT<T> FFT<T>::computeFFT(const Image<T>& anImage)
//---------------------------------------------------------------------
{
#ifdef HAS_FFTW
    FFT fft;
    fft.m_origin_image_width  = anImage.getWidth();
    fft.m_origin_image_height = anImage.getHeight();

    unsigned int width_power_of_two(powerOfTwo(fft.m_origin_image_width));
    unsigned int height_power_of_two(powerOfTwo(fft.m_origin_image_height));

    if (width_power_of_two != 1)
    {
        width_power_of_two = (std::max(width_power_of_two, height_power_of_two));
    }

    if (height_power_of_two != 1)
    {
        height_power_of_two = (std::max(width_power_of_two, height_power_of_two));
    }

    fft.m_real = Image<T>(width_power_of_two, height_power_of_two, anImage.getDepth());
    fft.m_img  = Image<T>(width_power_of_two, height_power_of_two, anImage.getDepth());

    fftw_complex *in_src, *out_src;
    fftw_plan p_forw;

    in_src  = reinterpret_cast<fftw_complex*>(fftw_malloc(sizeof(fftw_complex) * width_power_of_two * height_power_of_two));
    out_src = reinterpret_cast<fftw_complex*>(fftw_malloc(sizeof(fftw_complex) * width_power_of_two * height_power_of_two));

    if (width_power_of_two == 1 ||  height_power_of_two == 1)
    {
        p_forw = fftw_plan_dft_1d(std::max(width_power_of_two, height_power_of_two), in_src, out_src, FFTW_FORWARD, FFTW_ESTIMATE);
    }
    else
    {
        p_forw = fftw_plan_dft_2d(width_power_of_two, height_power_of_two, in_src, out_src, FFTW_FORWARD, FFTW_ESTIMATE);
    }

    //float max_value(anImage.getMaxValue());
    bool y_forward_copy(false);
    int j2(0);

    for (unsigned int k(0); k < anImage.getDepth(); ++k)
    {
        for (int j1 = 0 ; j1 < height_power_of_two ; ++j1)
        {
            if (!(j1 % fft.m_origin_image_height))
            {
                y_forward_copy = !y_forward_copy;

                if (y_forward_copy)
                {
                    j2 = 0;
                }
                else
                {
                    j2 = fft.m_origin_image_height - 1;
                }
            }

            bool x_forward_copy(false);
            int i2(0);
            for (int i1 = 0 ; i1 < width_power_of_two ; ++i1)
            {
                if (!(i1 % fft.m_origin_image_width))
                {
                    x_forward_copy = !x_forward_copy;

                    if (x_forward_copy)
                    {
                        i2 = 0;
                    }
                    else
                    {
                        i2 = fft.m_origin_image_width - 1;
                    }
                }

                in_src[j1 * width_power_of_two + i1][0] = anImage(i2, j2, k);
                in_src[j1 * width_power_of_two + i1][1] = 0.0;

                if (x_forward_copy)
                {
                    ++i2;
                }
                else
                {
                    --i2;
                }
            }

            if (y_forward_copy)
            {
                ++j2;
            }
            else
            {
                --j2;
            }
        }

        // Compute the forward fft
        fftw_execute(p_forw);

        //double max_value(getMaxValue());
        double square_size(width_power_of_two * height_power_of_two);

        for (int j = 0 ; j < height_power_of_two ; ++j)
        {
            for (int i = 0 ; i < width_power_of_two ; ++i)
            {
                fft.m_real(i, j, k) = out_src[j * width_power_of_two + i][0] / square_size;
                fft.m_img( i, j, k) = out_src[j * width_power_of_two + i][1] / square_size;
            }
        }
    }

    fftw_destroy_plan(p_forw);
    fftw_free(in_src);
    fftw_free(out_src);

    return (fft);
#else // HAS_FFTW
throw Exception(__FILE__, __FUNCTION__, __LINE__, "FFTW not supported");
#endif // HAS_FFTW
}


//---------------------------------------------------------
template<typename T> Image<T> FFT<T>::getInverseFFT() const
//---------------------------------------------------------
{
#ifdef HAS_FFTW
    Image<T> temp(m_real.getWidth(), m_real.getHeight(), m_real.getDepth());

    // allocate input arrays
    fftw_complex *in_src, *out_src;
    fftw_plan p_back;

    in_src  = reinterpret_cast<fftw_complex*>(fftw_malloc(sizeof(fftw_complex) * m_real.getWidth() * m_real.getHeight()));
    out_src = reinterpret_cast<fftw_complex*>(fftw_malloc(sizeof(fftw_complex) * m_real.getWidth() * m_real.getHeight()));


    if (m_real.getWidth() == 1 ||  m_real.getHeight() == 1)
    {
        p_back = fftw_plan_dft_1d(std::max(m_real.getWidth(), m_real.getHeight()), in_src, out_src, FFTW_BACKWARD, FFTW_ESTIMATE);
    }
    else
    {
        p_back = fftw_plan_dft_2d(m_real.getWidth(), m_real.getHeight(), in_src, out_src, FFTW_BACKWARD, FFTW_ESTIMATE);
    }

    // transform magnitude/phase to real/imaginary
    for (unsigned int k(0); k < m_real.getDepth(); ++k)
    {
        for (unsigned int j(0); j < m_real.getHeight(); ++j)
        {
            for (unsigned int i(0); i < m_real.getWidth(); ++i)
            {
                in_src[j * m_real.getWidth() + i][0] = m_real(i, j, k);
                in_src[j * m_real.getWidth() + i][1] = m_img(i, j, k);
            }
        }

        // perform ift
        fftw_execute(p_back);

        // save real parts to output
        for (unsigned int j(0); j < m_real.getHeight(); ++j)
        {
            for (unsigned int i(0); i < m_real.getWidth(); ++i)
            {
                temp(i, j, k) = out_src[j * m_real.getWidth() + i][0];
            }
        }
    }


    // free memory
    fftw_destroy_plan(p_back);
    fftw_free(in_src); fftw_free(out_src);

    return (temp.getROI(0, 0, 0, m_origin_image_width, m_origin_image_height, m_real.getDepth()));
#else // HAS_FFTW
    throw Exception(__FILE__, __FUNCTION__, __LINE__, "FFTW not supported");
#endif // HAS_FFTW
}


//----------------------------------------------------
template<typename T> FFT<T> FFT<T>::filterRamp() const
//----------------------------------------------------
{
    FFT filtered_fft(*this);

    if (filtered_fft.m_real.getWidth() == 1 || filtered_fft.m_real.getHeight() == 1)
    {
        double half_size(std::max(filtered_fft.m_real.getWidth(), filtered_fft.m_real.getHeight()) / 2.0);

        for (unsigned int i(0); i < filtered_fft.m_real.getWidth() * filtered_fft.m_real.getHeight(); ++i)
        {
            double distance(std::abs(half_size - i));
            distance /= half_size;

            filtered_fft.m_real[i] *= 1.0 - distance;
            filtered_fft.m_img[ i] *= 1.0 - distance;
        }
    }
    else
    {
        double half_diagonal_size(std::sqrt(std::pow(filtered_fft.m_real.getWidth(), 2) + std::pow(filtered_fft.m_real.getHeight(), 2)) / 2.0);
        double half_size(filtered_fft.m_real.getWidth() / 2.0);

        for (unsigned int j(0); j < filtered_fft.m_real.getHeight(); ++j)
        {
            for (unsigned int i(0); i < filtered_fft.m_real.getWidth(); ++i)
            {
                double distance(std::sqrt(std::pow(half_size - i, 2) + std::pow(half_size - j, 2)));
                distance /= half_diagonal_size;

                filtered_fft.m_real(i, j) *= 1.0 - distance;
                filtered_fft.m_img(i, j) *= 1.0 - distance;
            }
        }
    }

    return (filtered_fft);
}


template<typename T> FFT<T> FFT<T>::rhoFilter(const std::string& aFilterType, float aScalingFactor)
{
    FFT<T> filtered_fft(*this);

    unsigned int size(filtered_fft.m_real.getWidth());
    unsigned int half_size(size / 2);

    std::vector<double> p_filter(half_size, 1.0);

    // Apply the ramp filter (Ram-Lal)

    if ((aFilterType != "none" && aFilterType != "None" && aFilterType != "NONE") ||
        aFilterType == "ramp" || aFilterType == "Ramp" || aFilterType == "RAMP")
    {
        for (unsigned int i(0); i < p_filter.size(); ++i)
        {
            double distance(std::abs(double(half_size - i)));
            distance /= half_size;
            distance = aScalingFactor * (1.0 - distance);

            p_filter[i] = distance;
        }
    }

    if (aFilterType == "hamming" || aFilterType == "Hamming" || aFilterType == "HAMMING")
    {
        int m(size);
        --m;

        for (unsigned int i(0); i < half_size; ++i)
        {
            //unsigned int index_i(i + half_size);

            float c1 = 1.0 - (0.54 - 0.46 * std::cos (2.0 * Pi * float(i) / float(m)));
            //float c2 = 0.54 - 0.46 * std::cos (2.0 * Pi * float(index_i) / float(m));

            p_filter[i] *= c1;
            //p_filter[index_i] *= c1;
        }
    }
    else if (aFilterType == "hann" || aFilterType == "Hann" || aFilterType == "HANN" || aFilterType == "hanning" || aFilterType == "Hanning" || aFilterType == "HANNING")
    {
        throw Exception(__FILE__, __FUNCTION__, __LINE__, "rho_filter: Unknown window type");
    }
    else if (aFilterType == "cosine" || aFilterType == "Cosine" || aFilterType == "COSINE")
    {
        //f = 0.5 * (0:length (rho) - 1)' / length (rho);
        //filt = fftshift (sin (2 * pi * f));
        throw Exception(__FILE__, __FUNCTION__, __LINE__, "rho_filter: Unknown window type");
    }
    else if (aFilterType == "shepp-logan" || aFilterType == "Shepp-logan" || aFilterType == "Shepp-Logan" || aFilterType == "SHEPP-LOGAN")
    {
        //f = (0:length (rho) / 2)' / length (rho);
        //filt = sin (pi * f) ./ (pi * f);
        //filt (1) = 1;
        //filt = [filt; filt(end - 1:-1:2)];
        throw Exception(__FILE__, __FUNCTION__, __LINE__, "rho_filter: Unknown window type");
    }
    else if (!(aFilterType == "ramp" || aFilterType == "Ramp" || aFilterType == "RAMP"))
    {
        throw Exception(__FILE__, __FUNCTION__, __LINE__, "rho_filter: Unknown window type");
    }
    
    for (unsigned int k(0); k < filtered_fft.m_real.getDepth(); ++k)
    {
        for (unsigned int j(0); j < filtered_fft.m_real.getHeight(); ++j)
        {
            for (unsigned int i(0); i < p_filter.size(); ++i)
            {
                filtered_fft.m_real(i, j, k) *= p_filter[i];
                filtered_fft.m_img( i, j, k) *= p_filter[i];

                filtered_fft.m_real(size - 1 - i, j, k) *= p_filter[i];
                filtered_fft.m_img( size - 1 - i, j, k) *= p_filter[i];
            }
        }
    }

    return (filtered_fft);
}


template<typename T> FFT<T> FFT<T>::rhoFilter(const char* aFilterType, float aScalingFactor)
{
    return (rhoFilter(std::string(aFilterType), aScalingFactor));
}


//-----------------------------
template<typename T> Image<T> FFT<T>::getMagnitude() const
//-----------------------------
{
    Image<T> temp(m_real.getWidth(), m_real.getHeight());

    double square_size(m_real.getWidth() * m_real.getHeight());

    for(int j  = 0 ; j < m_real.getHeight() ; ++j)
    {
        for(int i = 0 ; i < m_real.getWidth() ; ++i)
        {
            unsigned int index(j * m_real.getWidth() + i);
            double real(m_real[index] / square_size);
            double img(m_img[index] / square_size);

            temp[index] = std::sqrt(real * real + img * img);
        }
    }

    return (swapQuadrants(temp));
}



//-------------------------
template<typename T> Image<T> FFT<T>::getPhase() const
//-------------------------
{
    Image<T> temp(m_real.getWidth(), m_real.getHeight());

    double square_size(m_real.getWidth() * m_real.getHeight());

    for(int j  = 0 ; j < m_real.getHeight() ; ++j)
    {
        for(int i = 0 ; i < m_real.getWidth() ; ++i)
        {
            unsigned int index(j * m_real.getWidth() + i);
            double real(m_real[index] / square_size);
            double img(m_img[index] / square_size);

            // phase
            std::complex<double> complex_value(real, img);
            double phase_value = arg(complex_value) + Pi;

            temp[index] = (phase_value / (2.0 * Pi));
        }
    }

    return (swapQuadrants(temp));
}


template<typename T> unsigned int FFT<T>::powerOfTwo(unsigned int i)
{
    unsigned int j(1);

    while (j < i) j *= 2;

    return (j);
}


template<typename T> Image<T> FFT<T>::swapQuadrants(const Image<T>& anImage)
{
    Image<T> temp_image(anImage);

    // It is correct as the width is a power of two (even number)
    int half_width(temp_image.getWidth() / 2);

    // It is correct as the height is a power of two (even number)
    int half_height(temp_image.getHeight() / 2);

    if (temp_image.getWidth() == 1)
    {
        for(unsigned int i = 0; i < half_width; ++i)
        {
            // It is correct as the width is a power of two (even number)
            unsigned int index_i(i + half_width);

            float temp(temp_image[i]);
            temp_image[i] = temp_image[index_i];
            temp_image[index_i] = temp;
        }
    }
    else if (temp_image.getHeight() == 1)
    {
        for(unsigned int j = 0; j < half_height; ++j)
        {
            // It is correct as the height is a power of two (even number)
            unsigned int index_j(j + half_height);

            float temp(temp_image[j * temp_image.getWidth()]);
            temp_image[j * temp_image.getWidth()] = temp_image[index_j * temp_image.getWidth()];
            temp_image[index_j * temp_image.getWidth()] = temp;
            }
    }
    else
    {
        // swap quadrants diagonally
        for(unsigned int j = 0; j < half_height; ++j)
        {
            // It is correct as the height is a power of two (even number)
            unsigned int index_j(j + half_height);

            for(unsigned int i = 0; i < half_width; ++i)
            {
                // It is correct as the width is a power of two (even number)
                unsigned int index_i(i + half_width);

                float temp(temp_image[j * temp_image.getWidth() + i]);
                temp_image[j * temp_image.getWidth() + i] = temp_image[index_j * temp_image.getWidth() + index_i];
                temp_image[index_j * temp_image.getWidth() + index_i] = temp;

                temp = temp_image[index_j * temp_image.getWidth() + i];
                temp_image[index_j * temp_image.getWidth() + i] = temp_image[j * temp_image.getWidth() + index_i];
                temp_image[j * temp_image.getWidth() + index_i] = temp;
            }
        }
    }

    return (temp_image);
}


} // namespace gVirtualXRay