pynufft_gpu.py 文件源码

def nufft_alpha_kb_fit(N, J, K):
    '''
    find out parameters alpha and beta
    of scaling factor st['sn']
    Note, when J = 1 , alpha is hardwired as [1,0,0...]
    (uniform scaling factor)
    '''
    beta = 1
    Nmid = (N - 1.0) / 2.0
    if N > 40:
        L = 13
    else:
        L = numpy.ceil(N / 3)

    nlist = numpy.arange(0, N) * 1.0 - Nmid
    (kb_a, kb_m) = kaiser_bessel('string', J, 'best', 0, K / N)
    if J > 1:
        sn_kaiser = 1 / kaiser_bessel_ft(nlist / K, J, kb_a, kb_m, 1.0)
    elif J == 1:  # The case when samples are on regular grids
        sn_kaiser = numpy.ones((1, N), dtype=dtype)
    gam = 2 * numpy.pi / K
    X_ant = beta * gam * nlist.reshape((N, 1), order='F')
    X_post = numpy.arange(0, L + 1)
    X_post = X_post.reshape((1, L + 1), order='F')
    X = numpy.dot(X_ant, X_post)  # [N,L]
    X = numpy.cos(X)
    sn_kaiser = sn_kaiser.reshape((N, 1), order='F').conj()
    X = numpy.array(X, dtype=dtype)
    sn_kaiser = numpy.array(sn_kaiser, dtype=dtype)
    coef = numpy.linalg.lstsq(numpy.nan_to_num(X), numpy.nan_to_num(sn_kaiser))[0]  # (X \ sn_kaiser.H);
    alphas = coef
    if J > 1:
        alphas[0] = alphas[0]
        alphas[1:] = alphas[1:] / 2.0
    elif J == 1:  # cases on grids
        alphas[0] = 1.0
        alphas[1:] = 0.0
    alphas = numpy.real(alphas)
    return (alphas, beta)