Working version of RSPA

src/hyperspectral/hyperspectral/unmixing/__init__.py

@@ -0,0 +1 @@
+from .rspa import rspa

src/hyperspectral/hyperspectral/unmixing/rspa.py

@@ -0,0 +1,55 @@
+import math
+
+import numpy as np
+
+def compute_alpha(x, y, β):
+    u = x / np.linalg.norm(x, 2)
+    assert np.linalg.norm(x, 2) > np.linalg.norm(y, 2), "x must be larger in norm than y"
+    num = (β * np.linalg.norm(x, 2)**2 - np.linalg.norm(y, 2)**2)
+    denom = (β * np.dot(u, x)**2 - np.dot(u, y)**2)
+    #print('Numerator:   {}\nDenominator: {}'.format(num, denom))
+    return 1 - math.sqrt(1 - num / denom)
+
+def select_key(spectra, d, p, β):
+    try:
+        from tqdm.autonotebook import trange
+    except:
+        trange = range
+
+    m = spectra.shape[1]
+    R = spectra
+    Y = R
+    Py = np.eye(m)
+    k = []
+    k1 = []
+    e = []
+    for i in trange(d, leave=False):
+        k.append(np.argmax(np.linalg.norm(Y, 2, axis=1)))
+        u = spectra[k[i]] / np.linalg.norm(spectra[k[i]], 2)
+        R = spectra - np.einsum('n,m->nm',np.matmul(spectra, u), u)
+        e.append(np.sum(np.linalg.norm(R, 2, axis=1)**p))
+        k1.append(np.argmax(np.linalg.norm(R, 2, axis=1)))
+        x = Y[k[i]]
+        y = Y[k1[i]]
+        #x = np.matmul(Py, spectra[k[i]])
+        #y = np.matmul(Py, spectra[k1[i]])
+        α = compute_alpha(x, y, β)
+        Y = Y - α * np.einsum('n,m->nm', np.matmul(Y, u), u)
+        #Py = np.matmul(np.eye(m) - α * np.outer(u, u), Py)
+    return k[np.argmin(e)]
+
+def rspa(image, n, d, β=4.0, p=1, tol=1e-8):
+    if len(image.shape)==3:
+        spectra = image.reshape((image.shape[0]*image.shape[1], -1))
+    else:
+        spectra = image
+    R = spectra
+    k = 1
+    keys = []
+    while np.any(np.abs(R) > tol) and k <= n:
+        key = select_key(R, d, p, β)
+        u = R[key] / np.linalg.norm(R[key], 2)
+        R = R - np.einsum('n,m->nm', np.matmul(R, u), u)
+        keys.append(key)
+        k = k + 1
+    return spectra[keys]

src/hyperspectral/requirements.txt

@@ -1,6 +1,7 @@
 GDAL==3.0.4
 jupyter==1.0.0
 matplotlib==3.1.2
+pysptools==0.15.0
 rasterio==1.1.7
 Shapely==1.7.1
 tqdm==4.51.0