def test_pywt_coeff_to_array_and_array_to_pywt_coeff():
# Verify that the helper function does indeed work as expected
wbasis = pywt.Wavelet('db1')
mode = 'zpd'
nscales = 2
n = 16
# 1D test
size_list = coeff_size_list((n,), nscales, wbasis, mode)
x = np.random.rand(n)
coeff_list = pywt.wavedec(x, wbasis, mode, nscales)
coeff_arr = pywt_coeff_to_array(coeff_list, size_list)
assert isinstance(coeff_arr, (np.ndarray))
length_of_array = np.prod(size_list[0])
length_of_array += sum(np.prod(shape) for shape in size_list[1:-1])
assert all_equal(len(coeff_arr), length_of_array)
coeff_list2 = array_to_pywt_coeff(coeff_arr, size_list)
assert all_equal(coeff_list, coeff_list2)
reconstruction = pywt.waverec(coeff_list2, wbasis, mode)
assert all_almost_equal(reconstruction, x)
# 2D test
size_list = coeff_size_list((n, n), nscales, wbasis, mode)
x = np.random.rand(n, n)
coeff_list = pywt.wavedec2(x, wbasis, mode, nscales)
coeff_arr = pywt_coeff_to_array(coeff_list, size_list)
assert isinstance(coeff_arr, (np.ndarray))
length_of_array = np.prod(size_list[0])
length_of_array += sum(3 * np.prod(shape) for shape in size_list[1:-1])
assert all_equal(len(coeff_arr), length_of_array)
coeff_list2 = array_to_pywt_coeff(coeff_arr, size_list)
assert all_equal(coeff_list, coeff_list2)
reconstruction = pywt.waverec2(coeff_list2, wbasis, mode)
assert all_almost_equal(reconstruction, x)
# 3D test
size_list = coeff_size_list((n, n, n), nscales, wbasis, mode)
x = np.random.rand(n, n, n)
coeff_dict = wavelet_decomposition3d(x, wbasis, mode, nscales)
coeff_arr = pywt_coeff_to_array(coeff_dict, size_list)
assert isinstance(coeff_arr, (np.ndarray))
length_of_array = np.prod(size_list[0])
length_of_array += sum(7 * np.prod(shape) for shape in size_list[1:-1])
assert len(coeff_arr) == length_of_array
coeff_dict2 = array_to_pywt_coeff(coeff_arr, size_list)
reconstruction = wavelet_reconstruction3d(coeff_dict2, wbasis, mode,
nscales)
assert all_equal(coeff_dict, coeff_dict)
assert all_almost_equal(reconstruction, x)
def test_pywt_coeff_to_array_and_array_to_pywt_coeff():
# Verify that the helper function does indeed work as expected
wbasis = pywt.Wavelet('db1')
mode = 'zpd'
nscales = 2
n = 16
# 1D test
size_list = coeff_size_list((n,), nscales, wbasis, mode)
x = np.random.rand(n)
coeff_list = pywt.wavedec(x, wbasis, mode, nscales)
coeff_arr = pywt_coeff_to_array(coeff_list, size_list)
assert isinstance(coeff_arr, (np.ndarray))
length_of_array = np.prod(size_list[0])
length_of_array += sum(np.prod(shape) for shape in size_list[1:-1])
assert all_equal(len(coeff_arr), length_of_array)
coeff_list2 = array_to_pywt_coeff(coeff_arr, size_list)
assert all_equal(coeff_list, coeff_list2)
reconstruction = pywt.waverec(coeff_list2, wbasis, mode)
assert all_almost_equal(reconstruction, x)
# 2D test
size_list = coeff_size_list((n, n), nscales, wbasis, mode)
x = np.random.rand(n, n)
coeff_list = pywt.wavedec2(x, wbasis, mode, nscales)
coeff_arr = pywt_coeff_to_array(coeff_list, size_list)
assert isinstance(coeff_arr, (np.ndarray))
length_of_array = np.prod(size_list[0])
length_of_array += sum(3 * np.prod(shape) for shape in size_list[1:-1])
assert all_equal(len(coeff_arr), length_of_array)
coeff_list2 = array_to_pywt_coeff(coeff_arr, size_list)
assert all_equal(coeff_list, coeff_list2)
reconstruction = pywt.waverec2(coeff_list2, wbasis, mode)
assert all_almost_equal(reconstruction, x)
# 3D test
size_list = coeff_size_list((n, n, n), nscales, wbasis, mode)
x = np.random.rand(n, n, n)
coeff_dict = wavelet_decomposition3d(x, wbasis, mode, nscales)
coeff_arr = pywt_coeff_to_array(coeff_dict, size_list)
assert isinstance(coeff_arr, (np.ndarray))
length_of_array = np.prod(size_list[0])
length_of_array += sum(7 * np.prod(shape) for shape in size_list[1:-1])
assert len(coeff_arr) == length_of_array
coeff_dict2 = array_to_pywt_coeff(coeff_arr, size_list)
reconstruction = wavelet_reconstruction3d(coeff_dict2, wbasis, mode,
nscales)
assert all_equal(coeff_dict, coeff_dict)
assert all_almost_equal(reconstruction, x)
def test_coeff_size_list():
# Verify that the helper function does indeed work as expected
shape = (16,)
nscale = 3
wbasis = pywt.Wavelet('db1')
mode = 'per'
size_list1d = coeff_size_list(shape, nscale, wbasis, mode)
S1d = [(2,), (2,), (4,), (8,), (16,)]
shape = (16, 16)
size_list2d = coeff_size_list(shape, nscale, wbasis, mode)
S2d = [(2, 2), (2, 2), (4, 4), (8, 8), (16, 16)]
shape = (16, 16, 16)
size_list3d = coeff_size_list(shape, nscale, wbasis, mode)
S3d = [(2, 2, 2), (2, 2, 2), (4, 4, 4), (8, 8, 8), (16, 16, 16)]
assert all_equal(size_list1d, S1d)
assert all_equal(size_list2d, S2d)
assert all_equal(size_list3d, S3d)
def test_coeff_size_list():
# Verify that the helper function does indeed work as expected
shape = (16,)
nscale = 3
wbasis = pywt.Wavelet('db1')
mode = 'per'
size_list1d = coeff_size_list(shape, nscale, wbasis, mode)
S1d = [(2,), (2,), (4,), (8,), (16,)]
shape = (16, 16)
size_list2d = coeff_size_list(shape, nscale, wbasis, mode)
S2d = [(2, 2), (2, 2), (4, 4), (8, 8), (16, 16)]
shape = (16, 16, 16)
size_list3d = coeff_size_list(shape, nscale, wbasis, mode)
S3d = [(2, 2, 2), (2, 2, 2), (4, 4, 4), (8, 8, 8), (16, 16, 16)]
assert all_equal(size_list1d, S1d)
assert all_equal(size_list2d, S2d)
assert all_equal(size_list3d, S3d)
def test_dwt():
# Verify that the operator works as axpected
# 1D test
n = 16
x = np.zeros(n)
x[5:10] = 1
wbasis = pywt.Wavelet('db1')
nscales = 2
mode = 'sym'
size_list = coeff_size_list((n,), nscales, wbasis, mode)
# Define a discretized domain
domain = odl.FunctionSpace(odl.Interval([-1], [1]))
nPoints = np.array([n])
disc_domain = odl.uniform_discr_fromspace(domain, nPoints)
disc_phantom = disc_domain.element(x)
# Create the discrete wavelet transform operator.
# Only the domain of the operator needs to be defined
Wop = DiscreteWaveletTransform(disc_domain, nscales, wbasis, mode)
# Compute the discrete wavelet transform of discrete imput image
coeffs = Wop(disc_phantom)
# Determine the correct range for Wop and verify that coeffs
# is an element of it
ran_size = np.prod(size_list[0])
ran_size += sum(np.prod(shape) for shape in size_list[1:-1])
disc_range = disc_domain.dspace_type(ran_size, dtype=disc_domain.dtype)
assert coeffs in disc_range
# Compute the inverse wavelet transform
reconstruction1 = Wop.inverse(coeffs)
# With othogonal wavelets the inverse is the adjoint
reconstruction2 = Wop.adjoint(coeffs)
# Verify that the output of Wop.inverse and Wop.adjoint are the same
assert all_almost_equal(reconstruction1.asarray(),
reconstruction2.asarray())
# Verify that reconstructions lie in correct discretized domain
assert reconstruction1 in disc_domain
assert reconstruction2 in disc_domain
assert all_almost_equal(reconstruction1.asarray(), x)
assert all_almost_equal(reconstruction2.asarray(), x)
# ---------------------------------------------------------------
# 2D test
n = 16
x = np.zeros((n, n))
x[5:10, 5:10] = 1
wbasis = pywt.Wavelet('db1')
nscales = 2
mode = 'sym'
size_list = coeff_size_list((n, n), nscales, wbasis, mode)
# Define a discretized domain
domain = odl.FunctionSpace(odl.Rectangle([-1, -1], [1, 1]))
nPoints = np.array([n, n])
disc_domain = odl.uniform_discr_fromspace(domain, nPoints)
disc_phantom = disc_domain.element(x)
# Create the discrete wavelet transform operator.
# Only the domain of the operator needs to be defined
Wop = DiscreteWaveletTransform(disc_domain, nscales, wbasis, mode)
# Compute the discrete wavelet transform of discrete imput image
coeffs = Wop(disc_phantom)
# Determine the correct range for Wop and verify that coeffs
# is an element of it
ran_size = np.prod(size_list[0])
ran_size += sum(3 * np.prod(shape) for shape in size_list[1:-1])
disc_range = disc_domain.dspace_type(ran_size, dtype=disc_domain.dtype)
assert coeffs in disc_range
# Compute the inverse wavelet transform
reconstruction1 = Wop.inverse(coeffs)
# With othogonal wavelets the inverse is the adjoint
reconstruction2 = Wop.adjoint(coeffs)
# Verify that the output of Wop.inverse and Wop.adjoint are the same
assert all_almost_equal(reconstruction1.asarray(),
reconstruction2.asarray())
# Verify that reconstructions lie in correct discretized domain
assert reconstruction1 in disc_domain
assert reconstruction2 in disc_domain
assert all_almost_equal(reconstruction1.asarray(), x)
assert all_almost_equal(reconstruction2.asarray(), x)
# -------------------------------------------------------------
# 3D test
n = 16
x = np.zeros((n, n, n))
x[5:10, 5:10, 5:10] = 1
wbasis = pywt.Wavelet('db2')
nscales = 1
mode = 'per'
size_list = coeff_size_list((n, n, n), nscales, wbasis, mode)
# Define a discretized domain
domain = odl.FunctionSpace(odl.Cuboid([-1, -1, -1], [1, 1, 1]))
nPoints = np.array([n, n, n])
disc_domain = odl.uniform_discr_fromspace(domain, nPoints)
disc_phantom = disc_domain.element(x)
# Create the discrete wavelet transform operator related to 3D transform.
Wop = DiscreteWaveletTransform(disc_domain, nscales, wbasis, mode)
# Compute the discrete wavelet transform of discrete imput image
coeffs = Wop(disc_phantom)
# Determine the correct range for Wop and verify that coeffs
# is an element of it
ran_size = np.prod(size_list[0])
ran_size += sum(7 * np.prod(shape) for shape in size_list[1:-1])
disc_range = disc_domain.dspace_type(ran_size, dtype=disc_domain.dtype)
assert coeffs in disc_range
# Compute the inverse wavelet transform
reconstruction1 = Wop.inverse(coeffs)
# With othogonal wavelets the inverse is the adjoint
reconstruction2 = Wop.adjoint(coeffs)
# Verify that the output of Wop.inverse and Wop.adjoint are the same
assert all_almost_equal(reconstruction1, reconstruction2)
# Verify that reconstructions lie in correct discretized domain
assert reconstruction1 in disc_domain
assert reconstruction2 in disc_domain
assert all_almost_equal(reconstruction1.asarray(), x)
assert all_almost_equal(reconstruction2, disc_phantom)
def test_dwt():
# Verify that the operator works as axpected
# 1D test
n = 16
x = np.zeros(n)
x[5:10] = 1
wbasis = pywt.Wavelet('db1')
nscales = 2
mode = 'sym'
size_list = coeff_size_list((n,), nscales, wbasis, mode)
# Define a discretized domain
domain = odl.FunctionSpace(odl.Interval([-1], [1]))
nPoints = np.array([n])
disc_domain = odl.uniform_discr_fromspace(domain, nPoints)
disc_phantom = disc_domain.element(x)
# Create the discrete wavelet transform operator.
# Only the domain of the operator needs to be defined
Wop = WaveletTransform(disc_domain, nscales, wbasis, mode)
# Compute the discrete wavelet transform of discrete imput image
coeffs = Wop(disc_phantom)
# Determine the correct range for Wop and verify that coeffs
# is an element of it
ran_size = np.prod(size_list[0])
ran_size += sum(np.prod(shape) for shape in size_list[1:-1])
disc_range = disc_domain.dspace_type(ran_size, dtype=disc_domain.dtype)
assert coeffs in disc_range
# Compute the inverse wavelet transform
reconstruction1 = Wop.inverse(coeffs)
# With othogonal wavelets the inverse is the adjoint
reconstruction2 = Wop.adjoint(coeffs)
# Verify that the output of Wop.inverse and Wop.adjoint are the same
assert all_almost_equal(reconstruction1.asarray(),
reconstruction2.asarray())
# Verify that reconstructions lie in correct discretized domain
assert reconstruction1 in disc_domain
assert reconstruction2 in disc_domain
assert all_almost_equal(reconstruction1.asarray(), x)
assert all_almost_equal(reconstruction2.asarray(), x)
# ---------------------------------------------------------------
# 2D test
n = 16
x = np.zeros((n, n))
x[5:10, 5:10] = 1
wbasis = pywt.Wavelet('db1')
nscales = 2
mode = 'sym'
size_list = coeff_size_list((n, n), nscales, wbasis, mode)
# Define a discretized domain
domain = odl.FunctionSpace(odl.Rectangle([-1, -1], [1, 1]))
nPoints = np.array([n, n])
disc_domain = odl.uniform_discr_fromspace(domain, nPoints)
disc_phantom = disc_domain.element(x)
# Create the discrete wavelet transform operator.
# Only the domain of the operator needs to be defined
Wop = WaveletTransform(disc_domain, nscales, wbasis, mode)
# Compute the discrete wavelet transform of discrete imput image
coeffs = Wop(disc_phantom)
# Determine the correct range for Wop and verify that coeffs
# is an element of it
ran_size = np.prod(size_list[0])
ran_size += sum(3 * np.prod(shape) for shape in size_list[1:-1])
disc_range = disc_domain.dspace_type(ran_size, dtype=disc_domain.dtype)
assert coeffs in disc_range
# Compute the inverse wavelet transform
reconstruction1 = Wop.inverse(coeffs)
# With othogonal wavelets the inverse is the adjoint
reconstruction2 = Wop.adjoint(coeffs)
# Verify that the output of Wop.inverse and Wop.adjoint are the same
assert all_almost_equal(reconstruction1.asarray(),
reconstruction2.asarray())
# Verify that reconstructions lie in correct discretized domain
assert reconstruction1 in disc_domain
assert reconstruction2 in disc_domain
assert all_almost_equal(reconstruction1.asarray(), x)
assert all_almost_equal(reconstruction2.asarray(), x)
# -------------------------------------------------------------
# 3D test
n = 16
x = np.zeros((n, n, n))
x[5:10, 5:10, 5:10] = 1
wbasis = pywt.Wavelet('db2')
nscales = 1
mode = 'per'
size_list = coeff_size_list((n, n, n), nscales, wbasis, mode)
# Define a discretized domain
domain = odl.FunctionSpace(odl.Cuboid([-1, -1, -1], [1, 1, 1]))
nPoints = np.array([n, n, n])
disc_domain = odl.uniform_discr_fromspace(domain, nPoints)
disc_phantom = disc_domain.element(x)
# Create the discrete wavelet transform operator related to 3D transform.
Wop = WaveletTransform(disc_domain, nscales, wbasis, mode)
# Compute the discrete wavelet transform of discrete imput image
coeffs = Wop(disc_phantom)
# Determine the correct range for Wop and verify that coeffs
# is an element of it
ran_size = np.prod(size_list[0])
ran_size += sum(7 * np.prod(shape) for shape in size_list[1:-1])
disc_range = disc_domain.dspace_type(ran_size, dtype=disc_domain.dtype)
assert coeffs in disc_range
# Compute the inverse wavelet transform
reconstruction1 = Wop.inverse(coeffs)
# With othogonal wavelets the inverse is the adjoint
reconstruction2 = Wop.adjoint(coeffs)
# Verify that the output of Wop.inverse and Wop.adjoint are the same
assert all_almost_equal(reconstruction1, reconstruction2)
# Verify that reconstructions lie in correct discretized domain
assert reconstruction1 in disc_domain
assert reconstruction2 in disc_domain
assert all_almost_equal(reconstruction1.asarray(), x)
assert all_almost_equal(reconstruction2, disc_phantom)