稀疏字典学习图像去噪

""" 项目内容：基于K-SVD学习的稀疏字典去噪 作者：忘川 时间：2019-03-11 """ import ImageProcessing as IP import math import cv2 import random from scipy import ndimage as nd import copy import numpy as np from PIL import Image as im """ 类说明：使用稀疏字典学习去噪 """ class SparseClearNoise (): """ 方法说明：初始化函数 参数说明：pic：无噪声图像 npic ：有噪声图像 返回值：无 """ def __init__ (self, pic,npic,samplek=1, sn=2): self.img = copy.deepcopy (pic) self.nimg = copy.deepcopy (npic) self.w = npic.shape[1] self.h = npic.shape[0] self.sn = sn self.nn = int((self.img.shape[1]-8)/self.sn) + 1 self.PicData = np.zeros((64,self.nn**2)) self.samplek = samplek """ 方法说明：创建一个DCT字典 参数说明：bs：大小 r；冗余系数 返回值：DCT：构建好的DCT """ def CreatDCT (self, bs=8, r=4): k = r*bs**2 hh = int (math.sqrt(k)) DCT = np.zeros((bs,hh)) for i in range(hh): V = np.cos(np.array([j*i*math.pi/hh for j in range(bs)])) if i > 0: V = V - np.mean(V) DCT[:,i] = V/np.linalg.norm(V) DCT = np.kron(DCT,DCT) ## V = np.array([[math.sqrt(2/bs)*math.cos(k*i*math.pi/bs/2)\ ## for k in range(16)] for i in range(bs)]) ## V[:,0] = V[:,0]/math.sqrt(2) ## for i in range(1,V.shape[1]): ## V[:,i] -= sum(V[:,i].tolist())/V.shape[0] ## avr = np.linalg.norm(V[:,i]) ## V[:,i] /= avr ## DCT = np.kron(V,V) return DCT """ 方法说明：以图像的形式显示一个字典 参数说明：DCT：被显示字典 ShowFlag：是否排序，只有学习后才使用排序 返回值：无 """ def ShowDCT (self, DCT, ShowFlag=0): a = [] D = copy.deepcopy(DCT) #归一化 for i in range (D.shape[1]): D[:,i] = D[:,i] - np.min(D[:,i]) if np.max(D[:,i]) != 0: D[:,i] = D[:,i]/np.max(D[:,i]) if ShowFlag == 1: P = np.var (D,axis=0)#列求平局值 for i in range (len (P)): maxn = np.argmax(P) a.extend([maxn]) P[maxn] = -P[maxn] I = np.zeros((D.shape[0],D.shape[1])) print (D) for i in range(D.shape[1]): I[:,i] = D[:,a[D.shape[1]-i-1]] D = I L = int(math.sqrt (DCT.shape[1])) n = int(math.sqrt (DCT.shape[0])) img_DCT = np.zeros((L*n,L*n)) for i in range(L): for j in range(L): for k in range (D.shape[0]): img_DCT[i*8+int(k%8)][j*8+int(k/8)] = D[k][i*16+j] img_DCT = img_DCT - np.min(D) img_DCT = img_DCT/np.max(D) img_DCT = np.uint8(img_DCT*255) print (img_DCT) ## image = im.fromarray(img_DCT.astype(np.int)) ## image.show() img_DCT1 = np.zeros((L*24,L*24),np.uint8) for i in range(L*8): for j in range(L*8): img_DCT1[i*3:i*3+3,j*3:j*3+3] = img_DCT[i][j] cv2.imshow ("DCT Image",img_DCT1) """ 方法说明：读取一副图像的数据，并以向量的形式给出。 参数说明：filename：图片数据的地址 返回值：PicData：图像数据 """ def GetPicInformation (self): nn = self.nn sn = self.sn k = 0 self.means = [] XY = [] self.index = np.zeros((self.img.shape[0],self.img.shape[0])) img = self.img for i in range(nn): for j in range(int(nn)):#先从坐到右，再从上到下 data8x8 = img[i*sn:i*sn+8,j*sn:j*sn+8] self.index[i*sn:i*sn+8,j*sn:j*sn+8] += np.array ([[1 for i in range(8)] for j in range (8)]) if self.samplek == 0: for ii in range(8): for jj in range(8): self.PicData[ii*8+jj][k] = data8x8[jj][ii] else: for ii in range(8): for jj in range(8): if ii%2 == 0: self.PicData[ii*8+jj][k] = data8x8[jj][ii] else: self.PicData[ii*8+jj][k] = data8x8[7-jj][ii] k += 1 for k in range(self.PicData.shape[1]):#将图片数据均一化 mean = np.mean(self.PicData[:,k]) self.means.extend ([mean])#求取列数据的均值，存储以备之后恢复使用 self.PicData[:,k] -= mean """ 方法说明：OMP算法计算系数系数 参数说明：dictionary：已经归一化的字典 dic:未经过归一化的字典 yr：对应的残差 ct；允许最小残差值(单个值的) 返回值：x：求得的稀疏稀疏 """ def Single_OMP (self,dictionary, dic, yr, ct): L = dictionary.shape[0] yrr = yr -np.zeros((L)) add = []#存放被选中原子的位置 A = np.empty(shape=(L,0))#存放被选出来的原子 r = np.linalg.norm(yrr) t = 0 ct = math.sqrt (ct**2*64) while t < 32 and r > ct:#进行算法求残差，求其稀疏 t += 1 product = np.dot(yrr.T,dictionary)#yr与字典取内积最大的向量 for i in range(len(product)): product[i] = abs(product[i]) maxn = np.argmax(product)#找到这行中最大的元素 add.extend([maxn])#存放位置信息 A = np.c_[A,dic[:,maxn]]#将内积最大的原子取出来放到新的矩阵中 #根据公式求残差 xr = np.dot(np.dot(np.linalg.inv(np.dot(A.T, A)), A.T), yr) yrr = yr - np.dot(A, xr) r = np.linalg.norm (yrr) #print ("ok") x = np.zeros ((256,1))#开始还原原来的稀疏 k = 0 for i in add:#读取指定位置的并将结果存放起来 x[i] = xr[k] k += 1 return x """ 方法说明：OMP算法计算稀疏系数 参数说明：dictionary：已经生成的字典 y：图像数据 ct：容许最大的残差 返回值：X:稀疏系数 """ def OMPLearning (self, dictionary, y, ct=10): X = np.empty (shape=(256,0))#存放所有的稀疏解 dic = copy.deepcopy(dictionary) for i in range(dictionary.shape[1]): avr = np.linalg.norm(dictionary[:,i])#求其列的模值 dictionary[:,i] = dictionary[:,i]/avr#列均一化处理 for i in range(y.shape[1]):#遍历所有的y列 xr = self.Single_OMP (dictionary, dic, y[:,i], ct)#计算每一列对应的稀疏稀疏 X = np.c_[X,xr]#稀疏解 return X """ 方法说明：K_SVD算法字典学习 参数说明：dictionary：已经生成的字典 y：图像数据 c：容许最大的残差 返回值：X:稀疏系数 首先如果残差设置太大可能会直接跳出循环 """ def K_SVDLearning (self, DCT, c=5, ct=15, num=4000): dictionary=copy.deepcopy(DCT) y=self.PicData ## ch = [random.randint(0,self.nn) for j in range (num)] ## y = np.zeros((64,num),np.uint8) ## for k in range(num):#随机抽取，进行K-SVD去噪 ## y.T[k] = yy.T[ch[k]] x=self.OMPLearning (dictionary, y, ct) for ci in range(c): ## fo