You can try with Imagemagick (https://legacy.imagemagick.org/Usage/fourier/#im_fft) :

    for quality in 50 75 90 95 99 ; do
      # FFT
      convert source.png -fft +depth +adjoin source_fft_%d.png
      
      # compress FFT magnitude and phase
      convert source_fft_0.png -quality $quality source_fft_magnitude.jpg
      convert source_fft_1.png -quality $quality     source_fft_phase.jpg
    
      # IFFT
      convert source_fft_magnitude.jpg source_fft_phase.jpg -ift out.$quality.png
    done