MATLAB实现k-svd和mod信号处理

function [Dictionary,output] = KSVD(... Data,... % an nXN matrix that contins N signals (Y), each of dimension n. param) % ========================================================================= % K-SVD algorithm % ========================================================================= % The K-SVD algorithm finds a dictionary for linear representation of % signals. Given a set of signals, it searches for the best dictionary that % can sparsely represent each signal. Detailed discussion on the algorithm % and possible applications can be found in "The K-SVD: An Algorithm for % Designing of Overcomplete Dictionaries for Sparse Representation", written % by M. Aharon, M. Elad, and A.M. Bruckstein and appeared in the IEEE Trans. % On Signal Processing, Vol. 54, no. 11, pp. 4311-4322, November 2006. % ========================================================================= % INPUT ARGUMENTS: % Data an nXN matrix that contins N signals (Y), each of dimension n. % param structure that includes all required % parameters for the K-SVD execution. % Required fields are: % K, ... the number of dictionary elements to train % K 原子个数 % numIteration,... number of iterations to perform. % numIteration 迭代次数 % errorFlag... if =0, a fix number of coefficients is % used for representation of each signal. If so, param.L must be % specified as the number of representing atom. if =1, arbitrary number % of atoms represent each signal, until a specific representation error % is reached. If so, param.errorGoal must be specified as the allowed % error. % preserveDCAtom... if =1 then the first atom in the dictionary % is set to be constant, and does not ever change. This % might be useful for working with natural % images (in this case, only param.K-1 % atoms are trained). % (optional, see errorFlag) L,... % maximum coefficients to use in OMP coefficient calculations. % (optional, see errorFlag) errorGoal, ... % allowed representation error in representing each signal. % InitializationMethod,... mehtod to initialize the dictionary, can % be one of the following arguments: % * 'DataElements' (initialization by the signals themselves), or: % * 'GivenMatrix' (initialization by a given matrix param.initialDictionary). % (optional, see InitializationMethod) initialDictionary,... % if the initialization method % is 'GivenMatrix', this is the matrix that will be used. % (optional) TrueDictionary, ... % if specified, in each % iteration the difference between this dictionary and the trained one % is measured and displayed. % displayProgress, ... if =1 progress information is displyed. If param.errorFlag==0, % the average repersentation error (RMSE) is displayed, while if % param.errorFlag==1, the average number of required coefficients for % representation of each signal is displayed. % ========================================================================= % OUTPUT ARGUMENTS: % Dictionary The extracted dictionary of size nX(param.K). % output Struct that contains information about the current run. It may include the following fields: % CoefMatrix The final coefficients matrix (it should hold that Data equals approximately Dictionary*output.CoefMatrix. % ratio If the true dictionary was defined (in % synthetic experiments), this parameter holds a vector of length % param.numIteration that includes the detection ratios in each % iteration). % totalerr The total representation error after each % iteration (defined only if % param.displayProgress=1 and % param.errorFlag = 0) % numCoef A vector of length param.numIteration that % include the average number of coefficients required for representation % of each signal (in each iteration) (defined only if % param.displayProgress=1 and % param.errorFlag = 1) % ========================================================================= %isfield(param,'displayProgress'):表示的是param中是否含有displayPrograess，如果含有则返回1，没有则返回0 if (~isfield(param,'displayProgress'))%%%原来的程序中含有param.displayProgress = displayFlag;%displayFlag = 1; 所以此句也不会执行 param.displayProgress = 0; end totalerr(1) = 99999;%代表的累积误差 if (isfield(param,'errorFlag')==0)%%%param.errorFlag = 1; 此句也不会执行 param.errorFlag = 0; end if (isfield(param,'TrueDictionary'))%%%param中没有TrueDictionary displayErrorWithTrueDictionary = 1; ErrorBetweenDictionaries = zeros(param.numIteration+1,1); ratio = zeros(param.numIteration+1,1); else displayErrorWithTrueDictionary = 0;%%执行此句 ratio = 0;%看开头的说明 end if (param.preserveDCAtom>0) %param.preserveDCAtom = 0; 表示是否保留第一个字典列向量 FixedDictionaryElement(1:size(Data,1),1) = 1/sqrt(size(Data,1)); else FixedDictionaryElement = [];%执行此句 end % coefficient calculation method is OMP with fixed number of coefficients if (size(Data,2) < param.K)% 这句的意思是判断原始数据的patch向量化以后的列数是否小于字典的原子数。 K=256 size(Data)=249*249 此句不满足if条件 disp('Size of data is smaller than the dictionary size. Trivial solution...'); Dictionary = Data(:,1:size(Data,2)); %如果小于就把原始数据向量化以后的矩阵作为字典 return; elseif (strcmp(param.InitializationMethod,'DataElements'))%%比较两个字符串是否相等 param.InitializationMethod = 'GivenMatrix'; Dictionary(:,1:param.K-param.preserveDCAtom) = Data(:,1:param.K-param.preserveDCAtom); elseif (strcmp(param.InitializationMethod,'GivenMatrix'))%% param.InitializationMethod = 'GivenMatrix'; 执行此句 Dictionary(:,1:param.K-param.preserveDCAtom) = param.initialDictionary(:,1:param.K-param.preserveDCAtom);%param.initialDictionary = DCT(:,1:param.K );%%%% 取了256列。也就是全部都取了 %param.preserveDCAtom=0 param.K-param.preserveDCAtom=K=256 初始化字典就是DCT字典 end % reduce the components in Dictionary that are spanned by the fixed % elements if (param.preserveDCAtom)% 这句是判断是否要保留字典的第一个原子不更新。 param.preserveDCAtom = 0; 此句不执行 tmpMat = FixedDictionaryElement \ Dictionary; Dictionary = Dictionary - FixedDictionaryElement*tmpMat; end %%进入正题了！！！！！ %normalize the dictionary. 对字典进行归一化 Dictionary = Dictionary*diag(1./sqrt(sum(Dictionary.*Dictionary)));%64*256 *256*256（可以借助帮助文档）：diag(1./sqrt(sum(Dictionary.*Dictionary))) 将sum(Dictionary.*Dictionary)作为对角线生成一个对角的矩阵 %上一句的作用：把Dictionary的每一列数据除以该列数据的平方和，从而进行归一化 Dictionary = Dictionary.*repmat(sign(Dictionary(1,:)),size(Dictionary,1),1); % multiply in the sign of the first element. 64*256 64*256 totalErr = zeros(1,param