Ejemplo n.º 1
0
def dtwaveifm(Yl,
              Yh,
              biort=DEFAULT_BIORT,
              qshift=DEFAULT_QSHIFT,
              gain_mask=None):
    """Perform an *n*-level dual-tree complex wavelet (DTCWT) 1D
    reconstruction.

    :param Yl: The real lowpass subband from the final level
    :param Yh: A sequence containing the complex highpass subband for each level.
    :param biort: Level 1 wavelets to use. See :py:func:`biort`.
    :param qshift: Level >= 2 wavelets to use. See :py:func:`qshift`.
    :param gain_mask: Gain to be applied to each subband.

    :returns Z: Reconstructed real array.
    
    The *l*-th element of *gain_mask* is gain for wavelet subband at level l.
    If gain_mask[l] == 0, no computation is performed for band *l*. Default
    *gain_mask* is all ones. Note that *l* is 0-indexed.

    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 reconstruction from Yl,Yh using the 13,19-tap filters 
        # for level 1 and the Q-shift 14-tap filters for levels >= 2.
        Z = dtwaveifm(Yl, Yh, 'near_sym_b', 'qshift_b')

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

    """
    a = len(Yh)  # No of levels.

    if gain_mask is None:
        gain_mask = np.ones(a)  # Default gain_mask.

    # 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

    level = a - 1  # No of levels = no of rows in L.
    if level < 0:
        # if there are no levels in the input, just return the Yl value
        return Yl

    Lo = Yl
    while level >= 1:  # Reconstruct levels 2 and above in reverse order.
        Hi = c2q1d(Yh[level] * gain_mask[level])
        Lo = colifilt(Lo, g0b, g0a) + colifilt(Hi, g1b, g1a)

        if Lo.shape[0] != 2 * Yh[level - 1].shape[
                0]:  # If Lo is not the same length as the next Yh => t1 was extended.
            Lo = Lo[
                1:-1,
                ...]  # Therefore we have to clip Lo so it is the same height as the next Yh.

        if np.any(
                np.asanyarray(Lo.shape) != np.asanyarray(Yh[level - 1].shape *
                                                         np.array((2, 1)))):
            raise ValueError('Yh sizes are not valid for DTWAVEIFM')

        level -= 1

    if level == 0:  # Reconstruct level 1.
        Hi = c2q1d(Yh[level] * gain_mask[level])
        Z = colfilter(Lo, g0o) + colfilter(Hi, g1o)

    # Return a 1d vector or a column vector
    if Z.shape[1] == 1:
        return Z.flatten()
    else:
        return Z
Ejemplo n.º 2
0
def dtwaveifm3(Yl, Yh, biort=DEFAULT_BIORT, qshift=DEFAULT_QSHIFT, ext_mode=4):
    """Perform an *n*-level dual-tree complex wavelet (DTCWT) 3D
    reconstruction.

    :param Yl: The real lowpass subband from the final level
    :param Yh: A sequence containing the complex highpass subband for each level.
    :param biort: Level 1 wavelets to use. See :py:func:`biort`.
    :param qshift: Level >= 2 wavelets to use. See :py:func:`qshift`.
    :param ext_mode: Extension mode. See below.

    :returns Z: Reconstructed real image matrix.

    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).

    There are two values for *ext_mode*, either 4 or 8. If *ext_mode* = 4,
    check whether 1st level is divisible by 2 (if not we raise a
    ``ValueError``). Also check whether from 2nd level onwards, the coefs can
    be divided by 4. If any dimension size is not a multiple of 4, append extra
    coefs by repeating the edges. If *ext_mode* = 8, check whether 1st level is
    divisible by 4 (if not we raise a ``ValueError``). Also check whether from
    2nd level onwards, the coeffs can be divided by 8. If any dimension size is
    not a multiple of 8, append extra coeffs by repeating the edges twice.

    Example::

        # Performs a 3-level reconstruction from Yl,Yh using the 13,19-tap
        # filters for level 1 and the Q-shift 14-tap filters for levels >= 2.
        Z = dtwaveifm3(Yl, Yh, 'near_sym_b', 'qshift_b')

    .. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
    .. codeauthor:: Huizhong Chen, Jan 2009
    .. codeauthor:: Nick Kingsbury, Cambridge University, July 1999.

    """
    # 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

    X = Yl

    nlevels = len(Yh)
    # level is 0-indexed but interpreted starting from the *last* level
    for level in xrange(nlevels):
        # Transform
        if level == nlevels-1: # non-obviously this is the 'first' level
            if Yh[-level-1] is None:
                Yl = _level1_ifm_no_highpass(Yl, g0o, g1o)
            else:
                Yl = _level1_ifm(Yl, Yh[-level-1], g0o, g1o)
        else:
            # Gracefully handle the Yh[0] is None case.
            if Yh[-level-2] is not None:
                prev_shape = Yh[-level-2].shape
            else:
                prev_shape = np.array(Yh[-level-1].shape) * 2

            Yl = _level2_ifm(Yl, Yh[-level-1], g0a, g0b, g1a, g1b, ext_mode, prev_shape)

    return Yl
Ejemplo n.º 3
0
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
Ejemplo n.º 4
0
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
Ejemplo n.º 5
0
def dtwavexfm3(X, nlevels=3, biort=DEFAULT_BIORT, qshift=DEFAULT_QSHIFT, ext_mode=4, discard_level_1=False):
    """Perform a *n*-level DTCWT-3D decompostion on a 3D matrix *X*.

    :param X: 3D real array-like object
    :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`.
    :param ext_mode: Extension mode. See below.
    :param discard_level_1: True if level 1 high-pass bands are to be discarded.

    :returns Yl: The real lowpass image from the final level
    :returns Yh: A tuple containing the complex highpass subimages for each level.

    Each element of *Yh* is a 4D complex array with the 4th dimension having
    size 28. The 3D slice ``Yh[l][:,:,:,d]`` corresponds to the complex higpass
    coefficients for direction d at level l where d and l are both 0-indexed.

    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).

    There are two values for *ext_mode*, either 4 or 8. If *ext_mode* = 4,
    check whether 1st level is divisible by 2 (if not we raise a
    ``ValueError``). Also check whether from 2nd level onwards, the coefs can
    be divided by 4. If any dimension size is not a multiple of 4, append extra
    coefs by repeating the edges. If *ext_mode* = 8, check whether 1st level is
    divisible by 4 (if not we raise a ``ValueError``). Also check whether from
    2nd level onwards, the coeffs can be divided by 8. If any dimension size is
    not a multiple of 8, append extra coeffs by repeating the edges twice.

    If *discard_level_1* is True the highpass coefficients at level 1 will be
    discarded. (And, in fact, will never be calculated.) This turns the
    transform from being 8:1 redundant to being 1:1 redundant at the cost of
    no-longer allowing perfect reconstruction. If this option is selected then
    `Yh[0]` will be `None`. Note that :py:func:`dtwaveifm3` will accepts
    `Yh[0]` being `None` and will treat it as being zero.

    Example::

        # Performs a 3-level transform on the real 3D array X using the 13,19-tap
        # filters for level 1 and the Q-shift 14-tap filters for levels >= 2.
        Yl, Yh = dtwavexfm3(X, 3, 'near_sym_b', 'qshift_b')

    .. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
    .. codeauthor:: Huizhong Chen, Jan 2009
    .. codeauthor:: Nick Kingsbury, Cambridge University, July 1999.

    """
    X = np.atleast_3d(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

    # Check value of ext_mode. TODO: this should really be an enum :S
    if ext_mode != 4 and ext_mode != 8:
        raise ValueError('ext_mode must be one of 4 or 8')

    Yl = X
    Yh = [None,] * nlevels

    # level is 0-indexed
    for level in xrange(nlevels):
        # Transform
        if level == 0 and discard_level_1:
            Yl = _level1_xfm_no_highpass(Yl, h0o, h1o, ext_mode)
        elif level == 0 and not discard_level_1:
            Yl, Yh[level] = _level1_xfm(Yl, h0o, h1o, ext_mode)
        else:
            Yl, Yh[level] = _level2_xfm(Yl, h0a, h0b, h1a, h1b, ext_mode)

    return Yl, tuple(Yh)
Ejemplo n.º 6
0
def dtwaveifm(Yl, Yh, biort=DEFAULT_BIORT, qshift=DEFAULT_QSHIFT, gain_mask=None):
    """Perform an *n*-level dual-tree complex wavelet (DTCWT) 1D
    reconstruction.

    :param Yl: The real lowpass subband from the final level
    :param Yh: A sequence containing the complex highpass subband for each level.
    :param biort: Level 1 wavelets to use. See :py:func:`biort`.
    :param qshift: Level >= 2 wavelets to use. See :py:func:`qshift`.
    :param gain_mask: Gain to be applied to each subband.

    :returns Z: Reconstructed real array.
    
    The *l*-th element of *gain_mask* is gain for wavelet subband at level l.
    If gain_mask[l] == 0, no computation is performed for band *l*. Default
    *gain_mask* is all ones. Note that *l* is 0-indexed.

    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 reconstruction from Yl,Yh using the 13,19-tap filters 
        # for level 1 and the Q-shift 14-tap filters for levels >= 2.
        Z = dtwaveifm(Yl, Yh, 'near_sym_b', 'qshift_b')

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

    """
    a = len(Yh) # No of levels.

    if gain_mask is None:
        gain_mask = np.ones(a) # Default gain_mask.

    # 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

    level = a-1   # No of levels = no of rows in L.
    if level < 0:
        # if there are no levels in the input, just return the Yl value
        return Yl

    Lo = Yl
    while level >= 1:  # Reconstruct levels 2 and above in reverse order.
       Hi = c2q1d(Yh[level]*gain_mask[level])
       Lo = colifilt(Lo, g0b, g0a) + colifilt(Hi, g1b, g1a)
       
       if Lo.shape[0] != 2*Yh[level-1].shape[0]:  # If Lo is not the same length as the next Yh => t1 was extended.
          Lo = Lo[1:-1,...]                       # Therefore we have to clip Lo so it is the same height as the next Yh.

       if np.any(np.asanyarray(Lo.shape) != np.asanyarray(Yh[level-1].shape * np.array((2,1)))):
          raise ValueError('Yh sizes are not valid for DTWAVEIFM')
       
       level -= 1

    if level == 0:  # Reconstruct level 1.
       Hi = c2q1d(Yh[level]*gain_mask[level])
       Z = colfilter(Lo,g0o) + colfilter(Hi,g1o)

    # Return a 1d vector or a column vector
    if Z.shape[1] == 1:
        return Z.flatten()
    else:
        return Z
Ejemplo n.º 7
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)
Ejemplo n.º 8
0
def dtwaveifm2(Yl,Yh,biort=DEFAULT_BIORT,qshift=DEFAULT_QSHIFT,gain_mask=None):
    """Perform an *n*-level dual-tree complex wavelet (DTCWT) 2D
    reconstruction.

    :param Yl: The real lowpass subband from the final level
    :param Yh: A sequence containing the complex highpass subband for each level.
    :param biort: Level 1 wavelets to use. See :py:func:`biort`.
    :param qshift: Level >= 2 wavelets to use. See :py:func:`qshift`.
    :param gain_mask: Gain to be applied to each subband.

    :returns Z: Reconstructed real array

    The (*d*, *l*)-th element of *gain_mask* is gain for subband with direction
    *d* at level *l*. If gain_mask[d,l] == 0, no computation is performed for
    band (d,l). Default *gain_mask* is all ones. Note that both *d* and *l* are
    zero-indexed.

    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 reconstruction from Yl,Yh using the 13,19-tap
        # filters for level 1 and the Q-shift 14-tap filters for levels >= 2.
        Z = dtwaveifm2(Yl, Yh, 'near_sym_b', 'qshift_b')

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

    """
    a = len(Yh) # No of levels.

    if gain_mask is None:
        gain_mask = np.ones((6,a)) # Default gain_mask.

    gain_mask = np.array(gain_mask)

    # 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

    current_level = a
    Z = Yl

    while current_level >= 2: # this ensures that for level 1 we never do the following
        lh = c2q(Yh[current_level-1][:,:,[0, 5]], gain_mask[[0, 5], current_level-1])
        hl = c2q(Yh[current_level-1][:,:,[2, 3]], gain_mask[[2, 3], current_level-1])
        hh = c2q(Yh[current_level-1][:,:,[1, 4]], gain_mask[[1, 4], current_level-1])

        # Do even Qshift filters on columns.
        y1 = colifilt(Z,g0b,g0a) + colifilt(lh,g1b,g1a)
        y2 = colifilt(hl,g0b,g0a) + colifilt(hh,g1b,g1a)

        # Do even Qshift filters on rows.
        Z = (colifilt(y1.T,g0b,g0a) + colifilt(y2.T,g1b,g1a)).T

        # Check size of Z and crop as required
        [row_size, col_size] = Z.shape
        S = 2*np.array(Yh[current_level-2].shape)
        if row_size != S[0]:    # check to see if this result needs to be cropped for the rows
            Z = Z[1:-1,:]
        if col_size != S[1]:    # check to see if this result needs to be cropped for the cols
            Z = Z[:,1:-1]

        if np.any(np.array(Z.shape) != S[:2]):
            raise ValueError('Sizes of subbands are not valid for DTWAVEIFM2')
        
        current_level = current_level - 1

    if current_level == 1:
        lh = c2q(Yh[current_level-1][:,:,[0, 5]],gain_mask[[0, 5],current_level-1])
        hl = c2q(Yh[current_level-1][:,:,[2, 3]],gain_mask[[2, 3],current_level-1])
        hh = c2q(Yh[current_level-1][:,:,[1, 4]],gain_mask[[1, 4],current_level-1])

        # Do odd top-level filters on columns.
        y1 = colfilter(Z,g0o) + colfilter(lh,g1o)
        y2 = colfilter(hl,g0o) + colfilter(hh,g1o)

        # Do odd top-level filters on rows.
        Z = (colfilter(y1.T,g0o) + colfilter(y2.T,g1o)).T

    return Z
Ejemplo n.º 9
0
def dtwaveifm2(Yl, Yh, biort=DEFAULT_BIORT, qshift=DEFAULT_QSHIFT, gain_mask=None):
    """Perform an *n*-level dual-tree complex wavelet (DTCWT) 2D
    reconstruction.

    :param Yl: The real lowpass subband from the final level
    :param Yh: A sequence containing the complex highpass subband for each level.
    :param biort: Level 1 wavelets to use. See :py:func:`biort`.
    :param qshift: Level >= 2 wavelets to use. See :py:func:`qshift`.
    :param gain_mask: Gain to be applied to each subband.

    :returns Z: Reconstructed real array

    The (*d*, *l*)-th element of *gain_mask* is gain for subband with direction
    *d* at level *l*. If gain_mask[d,l] == 0, no computation is performed for
    band (d,l). Default *gain_mask* is all ones. Note that both *d* and *l* are
    zero-indexed.

    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 reconstruction from Yl,Yh using the 13,19-tap
        # filters for level 1 and the Q-shift 14-tap filters for levels >= 2.
        Z = dtwaveifm2(Yl, Yh, 'near_sym_b', 'qshift_b')

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

    """
    a = len(Yh)  # No of levels.

    if gain_mask is None:
        gain_mask = np.ones((6, a))  # Default gain_mask.

    gain_mask = np.array(gain_mask)

    # 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

    current_level = a
    Z = Yl

    while current_level >= 2:  # this ensures that for level 1 we never do the following
        lh = c2q(Yh[current_level - 1][:, :, [0, 5]], gain_mask[[0, 5], current_level - 1])
        hl = c2q(Yh[current_level - 1][:, :, [2, 3]], gain_mask[[2, 3], current_level - 1])
        hh = c2q(Yh[current_level - 1][:, :, [1, 4]], gain_mask[[1, 4], current_level - 1])

        # Do even Qshift filters on columns.
        y1 = colifilt(Z, g0b, g0a) + colifilt(lh, g1b, g1a)
        y2 = colifilt(hl, g0b, g0a) + colifilt(hh, g1b, g1a)

        # Do even Qshift filters on rows.
        Z = (colifilt(y1.T, g0b, g0a) + colifilt(y2.T, g1b, g1a)).T

        # Check size of Z and crop as required
        [row_size, col_size] = Z.shape
        S = 2 * np.array(Yh[current_level - 2].shape)
        if row_size != S[0]:  # check to see if this result needs to be cropped for the rows
            Z = Z[1:-1, :]
        if col_size != S[1]:  # check to see if this result needs to be cropped for the cols
            Z = Z[:, 1:-1]

        if np.any(np.array(Z.shape) != S[:2]):
            raise ValueError("Sizes of subbands are not valid for DTWAVEIFM2")

        current_level = current_level - 1

    if current_level == 1:
        lh = c2q(Yh[current_level - 1][:, :, [0, 5]], gain_mask[[0, 5], current_level - 1])
        hl = c2q(Yh[current_level - 1][:, :, [2, 3]], gain_mask[[2, 3], current_level - 1])
        hh = c2q(Yh[current_level - 1][:, :, [1, 4]], gain_mask[[1, 4], current_level - 1])

        # Do odd top-level filters on columns.
        y1 = colfilter(Z, g0o) + colfilter(lh, g1o)
        y2 = colfilter(hl, g0o) + colfilter(hh, g1o)

        # Do odd top-level filters on rows.
        Z = (colfilter(y1.T, g0o) + colfilter(y2.T, g1o)).T

    return Z
Ejemplo n.º 10
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)