In [1]:
get_ipython().ast_node_interactivity = 'all' import os import matplotlib.pyplot as plt import numpy as np import matplotlib import math from PIL import Image import scipy.fftpack import scipy.optimize import random from sklearn.linear_model import Lasso matplotlib.rcParams['figure.dpi'] = 150 def show(img): _ = plt.imshow(img, cmap='gray') #_ = plt.colorbar() def img_open(path): img = Image.open(path) img = img.convert('L') while img.width * img.height > 100 * 100: img = img.resize((int(img.width / 1.1), int(img.height / 1.1))) return np.array(img, dtype=np.uint8)
In [2]:
target = img_open("/home/leo/Downloads/cat.jpg") W = target.shape[1] H = target.shape[0]
In [3]:
show(target)
Out:
In [4]:
received = int((W * H) * 0.25) not_received = (W * H) - received k = [True] * received + [False] * not_received random.shuffle(k) random.shuffle(k) random.shuffle(k) k = np.array(k)
In [5]:
show(target * k.reshape(target.shape))
Out:
In [11]:
b = target.T.flat[k] b = np.expand_dims(b, axis=1) b.shape A = np.kron( scipy.fftpack.idct(np.identity(W), norm='ortho', axis=0), scipy.fftpack.idct(np.identity(H), norm='ortho', axis=0) ) A = A[k,:] # same as phi times kron A.shape lasso = Lasso(alpha=0.001) lasso.fit(A, b)
Out [11]:
(2180, 1)
Out [11]:
(2180, 8720)
Out [11]:
Lasso(alpha=0.001)
In [7]:
def idct2(x): return scipy.fftpack.idct(scipy.fftpack.idct(x.T, norm='ortho', axis=0).T, norm='ortho', axis=0) Xat = np.array(lasso.coef_).reshape(W, H).T # stack columns # Get the reconstructed image Xa = idct2(Xat) # normalize _min = np.min(Xa) _max = np.max(Xa) Xa = np.interp(Xa, (_min, _max), (0, 1)) show(Xa)
Out:
