/usr/share/pyshared/pywt/multidim.py is in python-pywt 0.2.2-2.
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# Copyright (c) 2006-2012 Filip Wasilewski <http://en.ig.ma/>
# See COPYING for license details.
"""
2D Discrete Wavelet Transform and Inverse Discrete Wavelet Transform.
"""
__all__ = ['dwt2', 'idwt2', 'swt2', 'dwtn']
from itertools import izip, cycle
from _pywt import Wavelet, MODES
from _pywt import dwt, idwt, swt, downcoef
from numerix import transpose, array, as_float_array, default_dtype,\
apply_along_axis
def dwt2(data, wavelet, mode='sym'):
"""
2D Discrete Wavelet Transform.
data - 2D array with input data
wavelet - wavelet to use (Wavelet object or name string)
mode - signal extension mode, see MODES
Returns approximation and three details 2D coefficients arrays.
The result form four 2D coefficients arrays organized in tuples:
(approximation,
(horizontal details,
vertical details,
diagonal details)
)
which sometimes is also interpreted as laid out in one 2D array
of coefficients, where:
-----------------
| | |
| A(LL) | H(LH) |
| | |
(A, (H, V, D)) <---> -----------------
| | |
| V(HL) | D(HH) |
| | |
-----------------
"""
data = as_float_array(data)
if len(data.shape) != 2:
raise ValueError("Expected 2D data array")
if not isinstance(wavelet, Wavelet):
wavelet = Wavelet(wavelet)
mode = MODES.from_object(mode)
# filter rows
H, L = [], []
for row in data:
cA, cD = dwt(row, wavelet, mode)
L.append(cA)
H.append(cD)
del data
# filter columns
H = transpose(H)
L = transpose(L)
LL, LH = [], []
for row in L:
cA, cD = dwt(array(row, default_dtype), wavelet, mode)
LL.append(cA)
LH.append(cD)
del L
HL, HH = [], []
for row in H:
cA, cD = dwt(array(row, default_dtype), wavelet, mode)
HL.append(cA)
HH.append(cD)
del H
# build result structure
# (approx., (horizontal, vertical, diagonal))
ret = (transpose(LL), (transpose(LH), transpose(HL), transpose(HH)))
return ret
def idwt2(coeffs, wavelet, mode='sym'):
"""
2D Inverse Discrete Wavelet Transform. Reconstruct data from coefficients
arrays.
coeffs - four 2D coefficients arrays arranged as follows (in the same way
as dwt2 output -- see dwt2 description for details):
(approximation,
(horizontal details,
vertical details,
diagonal details)
)
wavelet - wavelet to use (Wavelet object or name string)
mode - signal extension mode, see MODES
"""
if len(coeffs) != 2 or len(coeffs[1]) != 3:
raise ValueError("Invalid coeffs param")
# L -low-pass data, H - high-pass data
LL, (LH, HL, HH) = coeffs
if LL is not None:
LL = transpose(LL)
if LH is not None:
LH = transpose(LH)
if HL is not None:
HL = transpose(HL)
if HH is not None:
HH = transpose(HH)
all_none = True
for arr in (LL, LH, HL, HH):
if arr is not None:
all_none = False
if len(arr.shape) != 2:
raise TypeError("All input coefficients arrays must be 2D.")
del arr
if all_none:
raise ValueError(
"At least one input coefficients array must not be None.")
if not isinstance(wavelet, Wavelet):
wavelet = Wavelet(wavelet)
mode = MODES.from_object(mode)
# idwt columns
L = []
if LL is None and LH is None:
L = None
else:
if LL is None:
# IDWT can handle None input values - equals to zero-array
LL = cycle([None])
if LH is None:
# IDWT can handle None input values - equals to zero-array
LH = cycle([None])
for rowL, rowH in izip(LL, LH):
L.append(idwt(rowL, rowH, wavelet, mode, 1))
del LL, LH
H = []
if HL is None and HH is None:
H = None
else:
if HL is None:
# IDWT can handle None input values - equals to zero-array
HL = cycle([None])
if HH is None:
# IDWT can handle None input values - equals to zero-array
HH = cycle([None])
for rowL, rowH in izip(HL, HH):
H.append(idwt(rowL, rowH, wavelet, mode, 1))
del HL, HH
if L is not None:
L = transpose(L)
if H is not None:
H = transpose(H)
# idwt rows
data = []
if L is None:
# IDWT can handle None input values - equals to zero-array
L = cycle([None])
if H is None:
# IDWT can handle None input values - equals to zero-array
H = cycle([None])
for rowL, rowH in izip(L, H):
data.append(idwt(rowL, rowH, wavelet, mode, 1))
return array(data, default_dtype)
def _downcoef(data, wavelet, mode, type):
"""Adapts pywt.downcoef call for apply_along_axis"""
return downcoef(type, data, wavelet, mode, level=1)
def dwtn(data, wavelet, mode='sym'):
"""
Single-level n-dimensional Discrete Wavelet Transform.
data - n-dimensional array
wavelet - wavelet to use (Wavelet object or name string)
mode - signal extension mode, see MODES
Results are arranged in a dictionary, where key specifies
the transform type on each dimension and value is a n-dimensional
coefficients array.
For example, for a 2D case the result will look something like this:
{
'aa': <coeffs> # A(LL) - approx. on 1st dim, approx. on 2nd dim
'ad': <coeffs> # H(LH) - approx. on 1st dim, det. on 2nd dim
'da': <coeffs> # V(HL) - det. on 1st dim, approx. on 2nd dim
'dd': <coeffs> # D(HH) - det. on 1st dim, det. on 2nd dim
}
"""
data = as_float_array(data)
dim = len(data.shape)
coeffs = [('', data)]
for axis in range(dim):
new_coeffs = []
for subband, x in coeffs:
new_coeffs.extend([
(subband + 'a', apply_along_axis(_downcoef, axis,
x, wavelet, mode, 'a')),
(subband + 'd', apply_along_axis(_downcoef, axis,
x, wavelet, mode, 'd'))
])
coeffs = new_coeffs
return dict(coeffs)
def swt2(data, wavelet, level, start_level=0):
"""
2D Stationary Wavelet Transform.
data - 2D array with input data
wavelet - wavelet to use (Wavelet object or name string)
level - how many decomposition steps to perform
start_level - the level at which the decomposition will start
Returns list of approximation and details coefficients:
[
(cA_n,
(cH_n, cV_n, cD_n)
),
(cA_n+1,
(cH_n+1, cV_n+1, cD_n+1)
),
...,
(cA_n+level,
(cH_n+level, cV_n+level, cD_n+level)
)
]
where cA is approximation, cH is horizontal details, cV is
vertical details, cD is diagonal details and n is start_level.
"""
data = as_float_array(data)
if len(data.shape) != 2:
raise ValueError("Expected 2D data array")
if not isinstance(wavelet, Wavelet):
wavelet = Wavelet(wavelet)
ret = []
for i in range(start_level, start_level + level):
# filter rows
H, L = [], []
for row in data:
cA, cD = swt(row, wavelet, level=1, start_level=i)[0]
L.append(cA)
H.append(cD)
del data
# filter columns
H = transpose(H)
L = transpose(L)
LL, LH = [], []
for row in L:
cA, cD = swt(
array(row, default_dtype), wavelet, level=1, start_level=i
)[0]
LL.append(cA)
LH.append(cD)
del L
HL, HH = [], []
for row in H:
cA, cD = swt(
array(row, default_dtype), wavelet, level=1, start_level=i
)[0]
HL.append(cA)
HH.append(cD)
del H
# build result structure
# (approx., (horizontal, vertical, diagonal))
approx = transpose(LL)
ret.append((approx, (transpose(LH), transpose(HL), transpose(HH))))
# for next iteration
data = approx # noqa
return ret
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