Python numpy.fft.ifft2() Examples

def wiener_dft(im: np.ndarray, sigma: float) -> np.ndarray:
    """
    Adaptive Wiener filter applied to the 2D FFT of the image
    :param im: multidimensional array
    :param sigma: estimated noise power
    :return: filtered version of input im
    """
    noise_var = sigma ** 2
    h, w = im.shape

    im_noise_fft = fft2(im)
    im_noise_fft_mag = np.abs(im_noise_fft / (h * w) ** .5)

    im_noise_fft_mag_noise = wiener_adaptive(im_noise_fft_mag, noise_var)

    zeros_y, zeros_x = np.nonzero(im_noise_fft_mag == 0)

    im_noise_fft_mag[zeros_y, zeros_x] = 1
    im_noise_fft_mag_noise[zeros_y, zeros_x] = 0

    im_noise_fft_filt = im_noise_fft * im_noise_fft_mag_noise / im_noise_fft_mag
    im_noise_filt = np.real(ifft2(im_noise_fft_filt))

    return im_noise_filt.astype(np.float32) 

def crosscorr_2d(k1: np.ndarray, k2: np.ndarray) -> np.ndarray:
    """
    PRNU 2D cross-correlation
    :param k1: 2D matrix of size (h1,w1)
    :param k2: 2D matrix of size (h2,w2)
    :return: 2D matrix of size (max(h1,h2),max(w1,w2))
    """
    assert (k1.ndim == 2)
    assert (k2.ndim == 2)

    max_height = max(k1.shape[0], k2.shape[0])
    max_width = max(k1.shape[1], k2.shape[1])

    k1 -= k1.flatten().mean()
    k2 -= k2.flatten().mean()

    k1 = np.pad(k1, [(0, max_height - k1.shape[0]), (0, max_width - k1.shape[1])], mode='constant', constant_values=0)
    k2 = np.pad(k2, [(0, max_height - k2.shape[0]), (0, max_width - k2.shape[1])], mode='constant', constant_values=0)

    k1_fft = fft2(k1, )
    k2_fft = fft2(np.rot90(k2, 2), )

    return np.real(ifft2(k1_fft * k2_fft)).astype(np.float32) 

def get_numpy(shape, fftn_shape=None, **kwargs):
    import numpy.fft as numpy_fft

    f = {
        "fft2": numpy_fft.fft2,
        "ifft2": numpy_fft.ifft2,
        "rfft2": numpy_fft.rfft2,
        "irfft2": lambda X: numpy_fft.irfft2(X, s=shape),
        "fftshift": numpy_fft.fftshift,
        "ifftshift": numpy_fft.ifftshift,
        "fftfreq": numpy_fft.fftfreq,
    }
    if fftn_shape is not None:
        f["fftn"] = numpy_fft.fftn
    fft = SimpleNamespace(**f)

    return fft 

def get_scipy(shape, fftn_shape=None, **kwargs):
    import numpy.fft as numpy_fft
    import scipy.fftpack as scipy_fft

    # use numpy implementation of rfft2/irfft2 because they have not been
    # implemented in scipy.fftpack
    f = {
        "fft2": scipy_fft.fft2,
        "ifft2": scipy_fft.ifft2,
        "rfft2": numpy_fft.rfft2,
        "irfft2": lambda X: numpy_fft.irfft2(X, s=shape),
        "fftshift": scipy_fft.fftshift,
        "ifftshift": scipy_fft.ifftshift,
        "fftfreq": scipy_fft.fftfreq,
    }
    if fftn_shape is not None:
        f["fftn"] = scipy_fft.fftn
    fft = SimpleNamespace(**f)

    return fft 

def synthesize(f_hat, axes=(0, 1)):
        """
        :param f_hat:
        :param axis:
        :return:
        """

        size = np.prod([f_hat.shape[ax] for ax in axes])
        f_hat = ifftshift(f_hat * size, axes=axes)
        f = ifft2(f_hat, axes=axes)
        return f 

def ifftd(I, dims=None):

    # Compute fft
    if dims is None:
        X = ifftn(I)
    elif dims == 2:
        X = ifft2(I, axes=(0, 1))
    else:
        X = ifftn(I, axes=tuple(range(dims)))

    return X 

def xcorr(imageA, imageB):
    FimageA = _fft.fft2(imageA)
    CFimageB = _np.conj(_fft.fft2(imageB))
    return _fft.fftshift(
        _np.real(_fft.ifft2((FimageA * CFimageB)))
    ) / _np.sqrt(imageA.size) 

def fft_convolve2d(x,y):
    """ 2D convolution, using FFT"""
    fr = fft2(x)
    fr2 = fft2(y)
    cc = np.real(ifft2(fr*fr2))
    cc = fftshift(cc)
    return cc 

def fft_convolve2d(x,y):
    """
    2D convolution, using FFT
    """
    fr = fft2(x)
    fr2 = fft2(np.flipud(np.fliplr(y)))
    m,n = fr.shape
    cc = np.real(ifft2(fr*fr2))
    cc = np.roll(cc, - int(m / 2) + 1, axis=0)
    cc = np.roll(cc, - int(n / 2) + 1, axis=1)
    return cc 

def sheardec2D(X, shearletsystem):
    """Shearlet Decomposition function."""
    coeffs = np.zeros(shearletsystem.shearlets.shape, dtype=complex)
    Xfreq = fftshift(fft2(ifftshift(X)))
    for i in range(shearletsystem.nShearlets):
        coeffs[:, :, i] = fftshift(ifft2(ifftshift(Xfreq * np.conj(
                                   shearletsystem.shearlets[:, :, i]))))
    return coeffs.real 

def shearrec2D(coeffs, shearletsystem):
    """Shearlet Recovery function."""
    X = np.zeros(coeffs.shape[:2], dtype=complex)
    for i in range(shearletsystem.nShearlets):
        X = X + fftshift(fft2(
            ifftshift(coeffs[:, :, i]))) * shearletsystem.shearlets[:, :, i]
    return (fftshift(ifft2(ifftshift((
            X / shearletsystem.dualFrameWeights))))).real 

def sheardecadjoint2D(coeffs, shearletsystem):
    """Shearlet Decomposition adjoint function."""
    X = np.zeros(coeffs.shape[:2], dtype=complex)
    for i in range(shearletsystem.nShearlets):
        X = X + fftshift(fft2(
            ifftshift(coeffs[:, :, i]))) * np.conj(
            shearletsystem.shearlets[:, :, i])
    return (fftshift(ifft2(ifftshift(
            X / shearletsystem.dualFrameWeights)))).real 

def shearrecadjoint2D(X, shearletsystem):
    """Shearlet Recovery adjoint function."""
    coeffs = np.zeros(shearletsystem.shearlets.shape, dtype=complex)
    Xfreq = fftshift(fft2(ifftshift(X)))
    for i in range(shearletsystem.nShearlets):
        coeffs[:, :, i] = fftshift(ifft2(ifftshift(
            Xfreq * shearletsystem.shearlets[:, :, i])))
    return coeffs.real 

def gs(idata,itera=10, ia=None):
    """Gerchberg-Saxton algorithm to calculate DOEs
    
    Calculates the phase distribution in a object plane to obtain an 
    specific amplitude distribution in the target plane. It uses a 
    FFT to calculate the field propagation.
    The wavefront at the DOE plane is assumed as a plane wave.
    
    **ARGUMENTS:**
    
        ========== ========================================================
        idata      numpy array containing the target amplitude distribution 
        itera      Maximum number of iterations
        ia         Illumination amplitude at the hologram plane if not given
                   it is assumed to be a constant amplitude with a value
                   of 1. If given it should be an array with the same shape
                   of idata
        ========== ========================================================
    """
    
    if ia==None:
        inpa=ones(idata.shape)
    else:
        inpa=ia
    
    assert idata.shape==inpa.shape, "ia and idata must have the same dimensions"
    
    fdata=fftshift(fft2(ifftshift(idata)))
    e=1000
    ea=1000
    
    for i in range (itera):
        fdata=exp(1.j*angle(fdata))*inpa
        
        rdata=ifftshift(ifft2(fftshift(fdata)))
        e= (abs(rdata)-idata).std()
        if e>ea: 
            break
        ea=e
        rdata=exp(1.j*angle(rdata))*(idata)
        fdata=fftshift(fft2(ifftshift(rdata)))        
    
    fdata=exp(1.j*angle(fdata))
    return fdata*inpa 

def gs_mod(idata,itera=10,osize=256):
    """Modiffied Gerchberg-Saxton algorithm to calculate DOEs
    
    Calculates the phase distribution in a object plane to obtain an 
    specific amplitude distribution in the target plane. It uses a 
    FFT to calculate the field propagation.
    The wavefront at the DOE plane is assumed as a plane wave.
    This algorithm leaves a window around the image plane to allow the 
    noise to move there. It only optimises the center of the image.
    
    **ARGUMENTS:**
    
        ========== ======================================================
        idata      numpy array containing the target amplitude distribution 
        itera      Maximum number of iterations
        osize      Size of the center of the image to be optimized
                   It should be smaller than the image itself.
        ========== ======================================================
    """
    M,N=idata.shape
    cut=osize//2
    
    
    zone=zeros_like(idata)
    zone[M/2-cut:M/2+cut,N/2-cut:N/2+cut]=1
    zone=zone.astype(bool)

    mask=exp(2.j*pi*random(idata.shape))
    mask[zone]=0
    
    #~ imshow(abs(mask)),colorbar()
    
    fdata=fftshift(fft2(ifftshift(idata+mask))) #Nota, colocar esta mascara es muy importante, por que si no  no converge tan rapido
    
    e=1000
    ea=1000
    for i in range (itera):
        fdata=exp(1.j*angle(fdata))

        rdata=ifftshift(ifft2(fftshift(fdata)))
        #~ e= (abs(rdata[zone])-idata[zone]).std()
        #~ if e>ea: 
           #~ 
            #~ break
        ea=e
        rdata[zone]=exp(1.j*angle(rdata[zone]))*(idata[zone])        
        fdata=fftshift(fft2(ifftshift(rdata)))   
    fdata=exp(1.j*angle(fdata))
    return fdata