def pca_ring_spectrum(images, std=0):
"""
Decomposes a set of SEDs from multiband images into PCA and filters the less significant coefficients
INPUTS:
images: cube of muti-bandimages with size n1xn2xs where s is the number of bands and n1xn2, the size of each image
OUTPUTS:
alphas: PCA coefficients for each SED at each pixel location.
basis: corresponding PCA basis.
sig: noise as propagated into PCA space.
EXAMPLE:
"""
pad = 0
images = images.T
n1, n2, s = np.shape(images)
res0 = images + 0
res = res0 + 0
res1 = res + 0.
sigmamr = np.zeros(s)
tr = res + 0 #For thresholded images
support = np.zeros((n1, n2))
for j in range(s):
sigmamr[j] = MCA.MAD(res0[:, :, j])
res[:, :, j] = res1[:, :, j]
x, y = np.where(res[:, :, j] == 0)
tr[x, y, j] = 0
tr[:, :, -1] = 1
support = np.prod(tr, 2)
support[np.where(support == 0.0)] = 0
support[np.where(support != 0.0)] = 1
x00, y00 = np.where(support == 0)
res[x00, y00, :] = 0
x, y = np.where(support == 1)
support1d = np.reshape(support, (n1 * n2))
x1d = np.where(support1d == 1)
spectrums = np.reshape(res[x, y, :], (np.size(x1d), s))
alphas = np.zeros((np.size(x), n1 * n2))
alpha, base = mk.mk_pca(spectrums.T)
##Noise propagation in PCA space
noise = np.multiply(np.random.randn(100, s), std.T)
alphanoise = np.dot(base.T, noise.T)
sig = np.zeros(2)
sig[0] = np.std(alphanoise[0, :])
sig[1] = np.std(alphanoise[1, :])
count = 0
for ind in np.reshape(x1d, np.size(x1d)):
alphas[:, ind] = alpha[:, count]
count = count + 1
return alphas, base, sig
