Exemplo n.º 1
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def test_output_size():
    Y = coldfilt(lena, (-1,1), (1,-1))
    assert Y.shape == (lena.shape[0]/2, lena.shape[1])
Exemplo n.º 2
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def dtwavexfm(X,
              nlevels=3,
              biort=DEFAULT_BIORT,
              qshift=DEFAULT_QSHIFT,
              include_scale=False):
    """Perform a *n*-level DTCWT decompostion on a 1D column vector *X* (or on
    the columns of a matrix *X*).

    :param X: 1D real array or 2D real array whose columns are to be transformed
    :param nlevels: Number of levels of wavelet decomposition
    :param biort: Level 1 wavelets to use. See :py:func:`biort`.
    :param qshift: Level >= 2 wavelets to use. See :py:func:`qshift`.

    :returns Yl: The real lowpass image from the final level
    :returns Yh: A tuple containing the (N, M, 6) shape complex highpass subimages for each level.
    :returns Yscale: If *include_scale* is True, a tuple containing real lowpass coefficients for every scale.

    If *biort* or *qshift* are strings, they are used as an argument to the
    :py:func:`biort` or :py:func:`qshift` functions. Otherwise, they are
    interpreted as tuples of vectors giving filter coefficients. In the *biort*
    case, this should be (h0o, g0o, h1o, g1o). In the *qshift* case, this should
    be (h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b).

    Example::

        # Performs a 5-level transform on the real image X using the 13,19-tap
        # filters for level 1 and the Q-shift 14-tap filters for levels >= 2.
        Yl, Yh = dtwavexfm(X,5,'near_sym_b','qshift_b')

    .. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
    .. codeauthor:: Nick Kingsbury, Cambridge University, May 2002
    .. codeauthor:: Cian Shaffrey, Cambridge University, May 2002

    """
    # Need this because colfilter and friends assumes input is 2d
    X = asfarray(X)
    if len(X.shape) == 1:
        X = np.atleast_2d(X).T

    # Try to load coefficients if biort is a string parameter
    try:
        h0o, g0o, h1o, g1o = _biort(biort)
    except TypeError:
        h0o, g0o, h1o, g1o = biort

    # Try to load coefficients if qshift is a string parameter
    try:
        h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b = _qshift(qshift)
    except TypeError:
        h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b = qshift

    L = np.asanyarray(X.shape)

    # ensure that X is an even length, thus enabling it to be extended if needs be.
    if X.shape[0] % 2 != 0:
        raise ValueError('Size of input X must be a multiple of 2')

    if nlevels == 0:
        if include_scale:
            return X, (), ()
        else:
            return X, ()

    # initialise
    Yh = [
        None,
    ] * nlevels
    if include_scale:
        # This is only required if the user specifies scales are to be outputted
        Yscale = [
            None,
        ] * nlevels

    # Level 1.
    Hi = colfilter(X, h1o)
    Lo = colfilter(X, h0o)
    Yh[0] = Hi[::2, :] + 1j * Hi[1::2, :]  # Convert Hi to complex form.
    if include_scale:
        Yscale[0] = Lo

    # Levels 2 and above.
    for level in xrange(1, nlevels):
        # Check to see if height of Lo is divisable by 4, if not extend.
        if Lo.shape[0] % 4 != 0:
            Lo = np.vstack((Lo[0, :], Lo, Lo[-1, :]))

        Hi = coldfilt(Lo, h1b, h1a)
        Lo = coldfilt(Lo, h0b, h0a)

        Yh[level] = Hi[::2, :] + 1j * Hi[1::
                                         2, :]  # Convert Hi to complex form.
        if include_scale:
            Yscale[level] = Lo

    Yl = Lo

    if include_scale:
        return Yl, Yh, Yscale
    else:
        return Yl, Yh
Exemplo n.º 3
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def test_good_input_size():
    coldfilt(lena[:,:511], (-1,1), (1,-1))
Exemplo n.º 4
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def test_good_input_size_non_orthogonal():
    coldfilt(lena[:,:511], (1,1), (1,1))
Exemplo n.º 5
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def test_different_size():
    coldfilt(lena, (-0.5,-1,2,1,0.5), (-1,2,-1))
Exemplo n.º 6
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def test_bad_input_size():
    coldfilt(lena[:511,:], (-1,1), (1,-1))
Exemplo n.º 7
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def test_odd_filter():
    coldfilt(lena, (-1,2,-1), (-1,2,1))
Exemplo n.º 8
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def _level2_xfm(X, h0a, h0b, h1a, h1b, ext_mode):
    """Perform level 2 or greater of the 3d transform.

    """

    if ext_mode == 4:
        if X.shape[0] % 4 != 0:
            X = np.concatenate((X[[0],:,:], X, X[[-1],:,:]), 0)
        if X.shape[1] % 4 != 0:
            X = np.concatenate((X[:,[0],:], X, X[:,[-1],:]), 1)
        if X.shape[2] % 4 != 0:
            X = np.concatenate((X[:,:,[0]], X, X[:,:,[-1]]), 2)
    elif ext_mode == 8:
        if X.shape[0] % 8 != 0:
            X = np.concatenate((X[(0,0),:,:], X, X[(-1,-1),:,:]), 0)
        if X.shape[1] % 8 != 0:
            X = np.concatenate((X[:,(0,0),:], X, X[:,(-1,-1),:]), 1)
        if X.shape[2] % 8 != 0:
            X = np.concatenate((X[:,:,(0,0)], X, X[:,:,(-1,-1)]), 2)

    # Create work area
    work_shape = np.asanyarray(X.shape)
    work = np.zeros(work_shape, dtype=X.dtype)

    # Form some useful slices
    s0a = slice(None, work.shape[0] >> 1)
    s1a = slice(None, work.shape[1] >> 1)
    s2a = slice(None, work.shape[2] >> 1)
    s0b = slice(work.shape[0] >> 1, None)
    s1b = slice(work.shape[1] >> 1, None)
    s2b = slice(work.shape[2] >> 1, None)

    # Assign input
    work = X

    # Loop over 2nd dimension extracting 2D slice from first and 3rd dimensions
    for f in xrange(work.shape[1]):
        # extract slice (copy required because we overwrite the work array)
        y = work[:, f, :].T.copy()

        # Do even Qshift filters on 3rd dim.
        work[:, f, s2b] = coldfilt(y, h1b, h1a).T
        work[:, f, s2a] = coldfilt(y, h0b, h0a).T

    # Loop over 3rd dimension extracting 2D slice from first and 2nd dimensions
    for f in xrange(work.shape[2]):
        # Do even Qshift filters on rows.
        y1 = work[:, :, f].T
        y2 = np.vstack((coldfilt(y1, h0b, h0a), coldfilt(y1, h1b, h1a))).T

        # Do even Qshift filters on columns.
        work[s0a, :, f] = coldfilt(y2, h0b, h0a)
        work[s0b, :, f] = coldfilt(y2, h1b, h1a)

    # Return appropriate slices of output
    return (
        work[s0a, s1a, s2a],                # LLL
        np.concatenate((
            cube2c(work[s0a, s1b, s2a]),    # HLL
            cube2c(work[s0b, s1a, s2a]),    # LHL
            cube2c(work[s0b, s1b, s2a]),    # HHL
            cube2c(work[s0a, s1a, s2b]),    # LLH
            cube2c(work[s0a, s1b, s2b]),    # HLH
            cube2c(work[s0b, s1a, s2b]),    # LHH
            cube2c(work[s0b, s1b, s2b]),    # HLH
        ), axis=3)
    )
Exemplo n.º 9
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def dtwavexfm(X, nlevels=3, biort=DEFAULT_BIORT, qshift=DEFAULT_QSHIFT, include_scale=False):
    """Perform a *n*-level DTCWT decompostion on a 1D column vector *X* (or on
    the columns of a matrix *X*).

    :param X: 1D real array or 2D real array whose columns are to be transformed
    :param nlevels: Number of levels of wavelet decomposition
    :param biort: Level 1 wavelets to use. See :py:func:`biort`.
    :param qshift: Level >= 2 wavelets to use. See :py:func:`qshift`.

    :returns Yl: The real lowpass image from the final level
    :returns Yh: A tuple containing the (N, M, 6) shape complex highpass subimages for each level.
    :returns Yscale: If *include_scale* is True, a tuple containing real lowpass coefficients for every scale.

    If *biort* or *qshift* are strings, they are used as an argument to the
    :py:func:`biort` or :py:func:`qshift` functions. Otherwise, they are
    interpreted as tuples of vectors giving filter coefficients. In the *biort*
    case, this should be (h0o, g0o, h1o, g1o). In the *qshift* case, this should
    be (h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b).

    Example::

        # Performs a 5-level transform on the real image X using the 13,19-tap
        # filters for level 1 and the Q-shift 14-tap filters for levels >= 2.
        Yl, Yh = dtwavexfm(X,5,'near_sym_b','qshift_b')

    .. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
    .. codeauthor:: Nick Kingsbury, Cambridge University, May 2002
    .. codeauthor:: Cian Shaffrey, Cambridge University, May 2002

    """
    # Need this because colfilter and friends assumes input is 2d
    X = asfarray(X)
    if len(X.shape) == 1:
       X = np.atleast_2d(X).T

    # Try to load coefficients if biort is a string parameter
    try:
        h0o, g0o, h1o, g1o = _biort(biort)
    except TypeError:
        h0o, g0o, h1o, g1o = biort

    # Try to load coefficients if qshift is a string parameter
    try:
        h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b = _qshift(qshift)
    except TypeError:
        h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b = qshift

    L = np.asanyarray(X.shape)

    # ensure that X is an even length, thus enabling it to be extended if needs be.
    if X.shape[0] % 2 != 0:
        raise ValueError('Size of input X must be a multiple of 2')

    if nlevels == 0:
        if include_scale:
            return X, (), ()
        else:
            return X, ()

    # initialise
    Yh = [None,] * nlevels
    if include_scale:
        # This is only required if the user specifies scales are to be outputted
        Yscale = [None,] * nlevels

    # Level 1.
    Hi = colfilter(X, h1o)  
    Lo = colfilter(X, h0o)
    Yh[0] = Hi[::2,:] + 1j*Hi[1::2,:] # Convert Hi to complex form.
    if include_scale:
        Yscale[0] = Lo

    # Levels 2 and above.
    for level in xrange(1, nlevels):
        # Check to see if height of Lo is divisable by 4, if not extend.
        if Lo.shape[0] % 4 != 0:
            Lo = np.vstack((Lo[0,:], Lo, Lo[-1,:]))

        Hi = coldfilt(Lo,h1b,h1a)
        Lo = coldfilt(Lo,h0b,h0a)

        Yh[level] = Hi[::2,:] + 1j*Hi[1::2,:] # Convert Hi to complex form.
        if include_scale:
            Yscale[level] = Lo

    Yl = Lo

    if include_scale:
        return Yl, Yh, Yscale
    else:
        return Yl, Yh
Exemplo n.º 10
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def dtwavexfm2(X, nlevels=3, biort=DEFAULT_BIORT, qshift=DEFAULT_QSHIFT, include_scale=False):
    """Perform a *n*-level DTCWT-2D decompostion on a 2D matrix *X*.

    :param X: 2D real array
    :param nlevels: Number of levels of wavelet decomposition
    :param biort: Level 1 wavelets to use. See :py:func:`biort`.
    :param qshift: Level >= 2 wavelets to use. See :py:func:`qshift`.

    :returns Yl: The real lowpass image from the final level
    :returns Yh: A tuple containing the complex highpass subimages for each level.
    :returns Yscale: If *include_scale* is True, a tuple containing real lowpass coefficients for every scale.

    If *biort* or *qshift* are strings, they are used as an argument to the
    :py:func:`biort` or :py:func:`qshift` functions. Otherwise, they are
    interpreted as tuples of vectors giving filter coefficients. In the *biort*
    case, this should be (h0o, g0o, h1o, g1o). In the *qshift* case, this should
    be (h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b).

    Example::

        # Performs a 3-level transform on the real image X using the 13,19-tap
        # filters for level 1 and the Q-shift 14-tap filters for levels >= 2.
        Yl, Yh = dtwavexfm2(X, 3, 'near_sym_b', 'qshift_b')

    .. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
    .. codeauthor:: Nick Kingsbury, Cambridge University, Sept 2001
    .. codeauthor:: Cian Shaffrey, Cambridge University, Sept 2001

    """
    X = np.atleast_2d(asfarray(X))

    # Try to load coefficients if biort is a string parameter
    try:
        h0o, g0o, h1o, g1o = _biort(biort)
    except TypeError:
        h0o, g0o, h1o, g1o = biort

    # Try to load coefficients if qshift is a string parameter
    try:
        h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b = _qshift(qshift)
    except TypeError:
        h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b = qshift

    original_size = X.shape

    if len(X.shape) >= 3:
        raise ValueError('The entered image is {0}, please enter each image slice separately.'.
                format('x'.join(list(str(s) for s in X.shape))))

    # The next few lines of code check to see if the image is odd in size, if so an extra ...
    # row/column will be added to the bottom/right of the image
    initial_row_extend = 0  #initialise
    initial_col_extend = 0
    if original_size[0] % 2 != 0:
        # if X.shape[0] is not divisable by 2 then we need to extend X by adding a row at the bottom
        X = np.vstack((X, X[[-1],:]))  # Any further extension will be done in due course.
        initial_row_extend = 1

    if original_size[1] % 2 != 0:
        # if X.shape[1] is not divisable by 2 then we need to extend X by adding a col to the left
        X = np.hstack((X, X[:,[-1]]))
        initial_col_extend = 1

    extended_size = X.shape

    if nlevels == 0:
        if include_scale:
            return X, (), ()
        else:
            return X, ()

    # initialise
    Yh = [None,] * nlevels
    if include_scale:
        # this is only required if the user specifies a third output component.
        Yscale = [None,] * nlevels

    complex_dtype = appropriate_complex_type_for(X)

    if nlevels >= 1:
        # Do odd top-level filters on cols.
        Lo = colfilter(X,h0o).T
        Hi = colfilter(X,h1o).T

        # Do odd top-level filters on rows.
        LoLo = colfilter(Lo,h0o).T
        Yh[0] = np.zeros((LoLo.shape[0] >> 1, LoLo.shape[1] >> 1, 6), dtype=complex_dtype)
        Yh[0][:,:,[0, 5]] = q2c(colfilter(Hi,h0o).T)     # Horizontal pair
        Yh[0][:,:,[2, 3]] = q2c(colfilter(Lo,h1o).T)     # Vertical pair
        Yh[0][:,:,[1, 4]] = q2c(colfilter(Hi,h1o).T)     # Diagonal pair

        if include_scale:
            Yscale[0] = LoLo

    for level in xrange(1, nlevels):
        row_size, col_size = LoLo.shape
        if row_size % 4 != 0:
            # Extend by 2 rows if no. of rows of LoLo are not divisable by 4
            LoLo = np.vstack((LoLo[[0],:], LoLo, LoLo[[-1],:]))

        if col_size % 4 != 0:
            # Extend by 2 cols if no. of cols of LoLo are not divisable by 4
            LoLo = np.hstack((LoLo[:,[0]], LoLo, LoLo[:,[-1]]))

        # Do even Qshift filters on rows.
        Lo = coldfilt(LoLo,h0b,h0a).T
        Hi = coldfilt(LoLo,h1b,h1a).T

        # Do even Qshift filters on columns.
        LoLo = coldfilt(Lo,h0b,h0a).T

        Yh[level] = np.zeros((LoLo.shape[0]>>1, LoLo.shape[1]>>1, 6), dtype=complex_dtype)
        Yh[level][:,:,[0, 5]] = q2c(coldfilt(Hi,h0b,h0a).T)  # Horizontal
        Yh[level][:,:,[2, 3]] = q2c(coldfilt(Lo,h1b,h1a).T)  # Vertical
        Yh[level][:,:,[1, 4]] = q2c(coldfilt(Hi,h1b,h1a).T)  # Diagonal   

        if include_scale:
            Yscale[0] = LoLo

    Yl = LoLo

    if initial_row_extend == 1 and initial_col_extend == 1:
        logging.warn('The image entered is now a {0} NOT a {1}.'.format(
            'x'.join(list(str(s) for s in extended_size)),
            'x'.join(list(str(s) for s in original_size))))
        logging.warn(
            'The bottom row and rightmost column have been duplicated, prior to decomposition.')

    if initial_row_extend == 1 and initial_col_extend == 0:
        logging.warn('The image entered is now a {0} NOT a {1}.'.format(
            'x'.join(list(str(s) for s in extended_size)),
            'x'.join(list(str(s) for s in original_size))))
        logging.warn(
            'The bottom row has been duplicated, prior to decomposition.')

    if initial_row_extend == 0 and initial_col_extend == 1:
        logging.warn('The image entered is now a {0} NOT a {1}.'.format(
            'x'.join(list(str(s) for s in extended_size)),
            'x'.join(list(str(s) for s in original_size))))
        logging.warn(
            'The rightmost column has been duplicated, prior to decomposition.')

    if include_scale:
        return Yl, tuple(Yh), tuple(Yscale)
    else:
        return Yl, tuple(Yh)
Exemplo n.º 11
0
def dtwavexfm2(X, nlevels=3, biort=DEFAULT_BIORT, qshift=DEFAULT_QSHIFT, include_scale=False):
    """Perform a *n*-level DTCWT-2D decompostion on a 2D matrix *X*.

    :param X: 2D real array
    :param nlevels: Number of levels of wavelet decomposition
    :param biort: Level 1 wavelets to use. See :py:func:`biort`.
    :param qshift: Level >= 2 wavelets to use. See :py:func:`qshift`.

    :returns Yl: The real lowpass image from the final level
    :returns Yh: A tuple containing the complex highpass subimages for each level.
    :returns Yscale: If *include_scale* is True, a tuple containing real lowpass coefficients for every scale.

    If *biort* or *qshift* are strings, they are used as an argument to the
    :py:func:`biort` or :py:func:`qshift` functions. Otherwise, they are
    interpreted as tuples of vectors giving filter coefficients. In the *biort*
    case, this should be (h0o, g0o, h1o, g1o). In the *qshift* case, this should
    be (h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b).

    Example::

        # Performs a 3-level transform on the real image X using the 13,19-tap
        # filters for level 1 and the Q-shift 14-tap filters for levels >= 2.
        Yl, Yh = dtwavexfm2(X, 3, 'near_sym_b', 'qshift_b')

    .. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
    .. codeauthor:: Nick Kingsbury, Cambridge University, Sept 2001
    .. codeauthor:: Cian Shaffrey, Cambridge University, Sept 2001

    """
    X = np.atleast_2d(asfarray(X))

    # Try to load coefficients if biort is a string parameter
    try:
        h0o, g0o, h1o, g1o = _biort(biort)
    except TypeError:
        h0o, g0o, h1o, g1o = biort

    # Try to load coefficients if qshift is a string parameter
    try:
        h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b = _qshift(qshift)
    except TypeError:
        h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b = qshift

    original_size = X.shape

    if len(X.shape) >= 3:
        raise ValueError(
            "The entered image is {0}, please enter each image slice separately.".format(
                "x".join(list(str(s) for s in X.shape))
            )
        )

    # The next few lines of code check to see if the image is odd in size, if so an extra ...
    # row/column will be added to the bottom/right of the image
    initial_row_extend = 0  # initialise
    initial_col_extend = 0
    if original_size[0] % 2 != 0:
        # if X.shape[0] is not divisable by 2 then we need to extend X by adding a row at the bottom
        X = np.vstack((X, X[[-1], :]))  # Any further extension will be done in due course.
        initial_row_extend = 1

    if original_size[1] % 2 != 0:
        # if X.shape[1] is not divisable by 2 then we need to extend X by adding a col to the left
        X = np.hstack((X, X[:, [-1]]))
        initial_col_extend = 1

    extended_size = X.shape

    if nlevels == 0:
        if include_scale:
            return X, (), ()
        else:
            return X, ()

    # initialise
    Yh = [None] * nlevels
    if include_scale:
        # this is only required if the user specifies a third output component.
        Yscale = [None] * nlevels

    complex_dtype = appropriate_complex_type_for(X)

    if nlevels >= 1:
        # Do odd top-level filters on cols.
        Lo = colfilter(X, h0o).T
        Hi = colfilter(X, h1o).T

        # Do odd top-level filters on rows.
        LoLo = colfilter(Lo, h0o).T
        Yh[0] = np.zeros((LoLo.shape[0] >> 1, LoLo.shape[1] >> 1, 6), dtype=complex_dtype)
        Yh[0][:, :, [0, 5]] = q2c(colfilter(Hi, h0o).T)  # Horizontal pair
        Yh[0][:, :, [2, 3]] = q2c(colfilter(Lo, h1o).T)  # Vertical pair
        Yh[0][:, :, [1, 4]] = q2c(colfilter(Hi, h1o).T)  # Diagonal pair

        if include_scale:
            Yscale[0] = LoLo

    for level in xrange(1, nlevels):
        row_size, col_size = LoLo.shape
        if row_size % 4 != 0:
            # Extend by 2 rows if no. of rows of LoLo are not divisable by 4
            LoLo = np.vstack((LoLo[[0], :], LoLo, LoLo[[-1], :]))

        if col_size % 4 != 0:
            # Extend by 2 cols if no. of cols of LoLo are not divisable by 4
            LoLo = np.hstack((LoLo[:, [0]], LoLo, LoLo[:, [-1]]))

        # Do even Qshift filters on rows.
        Lo = coldfilt(LoLo, h0b, h0a).T
        Hi = coldfilt(LoLo, h1b, h1a).T

        # Do even Qshift filters on columns.
        LoLo = coldfilt(Lo, h0b, h0a).T

        Yh[level] = np.zeros((LoLo.shape[0] >> 1, LoLo.shape[1] >> 1, 6), dtype=complex_dtype)
        Yh[level][:, :, [0, 5]] = q2c(coldfilt(Hi, h0b, h0a).T)  # Horizontal
        Yh[level][:, :, [2, 3]] = q2c(coldfilt(Lo, h1b, h1a).T)  # Vertical
        Yh[level][:, :, [1, 4]] = q2c(coldfilt(Hi, h1b, h1a).T)  # Diagonal

        if include_scale:
            Yscale[0] = LoLo

    Yl = LoLo

    if initial_row_extend == 1 and initial_col_extend == 1:
        logging.warn(
            "The image entered is now a {0} NOT a {1}.".format(
                "x".join(list(str(s) for s in extended_size)), "x".join(list(str(s) for s in original_size))
            )
        )
        logging.warn("The bottom row and rightmost column have been duplicated, prior to decomposition.")

    if initial_row_extend == 1 and initial_col_extend == 0:
        logging.warn(
            "The image entered is now a {0} NOT a {1}.".format(
                "x".join(list(str(s) for s in extended_size)), "x".join(list(str(s) for s in original_size))
            )
        )
        logging.warn("The bottom row has been duplicated, prior to decomposition.")

    if initial_row_extend == 0 and initial_col_extend == 1:
        logging.warn(
            "The image entered is now a {0} NOT a {1}.".format(
                "x".join(list(str(s) for s in extended_size)), "x".join(list(str(s) for s in original_size))
            )
        )
        logging.warn("The rightmost column has been duplicated, prior to decomposition.")

    if include_scale:
        return Yl, tuple(Yh), tuple(Yscale)
    else:
        return Yl, tuple(Yh)