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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def tikhonov_filter(s, lmbda, npd=16):
 r"""Lowpass filter based on Tikhonov regularization. Lowpass filter image(s) and return low and high frequency components, consisting of the lowpass filtered image and its difference with the input image. The lowpass filter is equivalent to Tikhonov regularization with `lmbda` as the regularization parameter and a discrete gradient as the operator in the regularization term, i.e. the lowpass component is the solution to .. math:: \mathrm{argmin}_\mathbf{x} \; (1/2) \left\|\mathbf{x} - \mathbf{s} \right\|_2^2 + (\lambda / 2) \sum_i \| G_i \mathbf{x} \|_2^2 \;\;, where :math:`\mathbf{s}` is the input image, :math:`\lambda` is the regularization parameter, and :math:`G_i` is an operator that computes the discrete gradient along image axis :math:`i`. Once the lowpass component :math:`\mathbf{x}` has been computed, the highpass component is just :math:`\mathbf{s} - \mathbf{x}`. Parameters s : array_like Input image or array of images. lmbda : float Regularization parameter controlling lowpass filtering. npd : int, optional (default=16) Number of samples to pad at image boundaries. Returns ------- sl : array_like Lowpass image or array of images. sh : array_like Highpass image or array of images. """


    grv = np.array([-1.0, 1.0]).reshape([2, 1])
    gcv = np.array([-1.0, 1.0]).reshape([1, 2])
    Gr = sla.fftn(grv, (s.shape[0] + 2*npd, s.shape[1] + 2*npd), (0, 1))
    Gc = sla.fftn(gcv, (s.shape[0] + 2*npd, s.shape[1] + 2*npd), (0, 1))
    A = 1.0 + lmbda*np.conj(Gr)*Gr + lmbda*np.conj(Gc)*Gc
    if s.ndim > 2:
        A = A[(slice(None),)*2 + (np.newaxis,)*(s.ndim-2)]
    sp = np.pad(s, ((npd, npd),)*2 + ((0, 0),)*(s.ndim-2), 'symmetric')
    slp = np.real(sla.ifftn(sla.fftn(sp, axes=(0, 1)) / A, axes=(0, 1)))
    sl = slp[npd:(slp.shape[0] - npd), npd:(slp.shape[1] - npd)]
    sh = s - sl
    return sl.astype(s.dtype), sh.astype(s.dtype)