Ultrasound-Image-reconstruction-master.zip_B扫_B扫成像_ultrasound_ul

function [z,s,exitflag,Wtot] = smoothn(varargin) %SMOOTHN Robust spline smoothing for 1-D to N-D data. % SMOOTHN provides a fast, automatized and robust discretized smoothing % spline for data of any dimension. % % Z = SMOOTHN(Y) automatically smoothes the uniformly-sampled array Y. Y % can be any N-D noisy array (time series, images, 3D data,...). Non % finite data (NaN or Inf) are treated as missing values. % % Z = SMOOTHN(Y,S) smoothes the array Y using the smoothing parameter S. % S must be a real positive scalar. The larger S is, the smoother the % output will be. If the smoothing parameter S is omitted (see previous % option) or empty (i.e. S = []), it is automatically determined using % the generalized cross-validation (GCV) method. % % Z = SMOOTHN(Y,W) or Z = SMOOTHN(Y,W,S) specifies a weighting array W of % real positive values, that must have the same size as Y. Note that a % nil weight corresponds to a missing value. % % Robust smoothing % ---------------- % Z = SMOOTHN(...,'robust') carries out a robust smoothing that minimizes % the influence of outlying data. % % [Z,S] = SMOOTHN(...) also returns the calculated value for S so that % you can fine-tune the smoothing subsequently if needed. % % An iteration process is used in the presence of weighted and/or missing % values. Z = SMOOTHN(...,OPTION_NAME,OPTION_VALUE) smoothes with the % termination parameters specified by OPTION_NAME and OPTION_VALUE. They % can contain the following criteria: % ----------------- % TolZ: Termination tolerance on Z (default = 1e-3) % TolZ must be in ]0,1[ % MaxIter: Maximum number of iterations allowed (default = 100) % Initial: Initial value for the iterative process (default = % original data) % ----------------- % Syntax: [Z,...] = SMOOTHN(...,'MaxIter',500,'TolZ',1e-4,'Initial',Z0); % % [Z,S,EXITFLAG] = SMOOTHN(...) returns a boolean value EXITFLAG that % describes the exit condition of SMOOTHN: % 1 SMOOTHN converged. % 0 Maximum number of iterations was reached. % % Class Support % ------------- % Input array can be numeric or logical. The returned array is of class % double. % % Notes % ----- % The N-D (inverse) discrete cosine transform functions <a % href="matlab:web('http://www.biomecardio.com/matlab/dctn.html')" % >DCTN</a> and <a % href="matlab:web('http://www.biomecardio.com/matlab/idctn.html')" % >IDCTN</a> are required. % % To be made % ---------- % Estimate the confidence bands (see Wahba 1983, Nychka 1988). % % Reference % --------- % Garcia D, Robust smoothing of gridded data in one and higher dimensions % with missing values. Computational Statistics & Data Analysis, 2010. % <a % href="matlab:web('http://www.biomecardio.com/pageshtm/publi/csda10.pdf')">PDF download</a> % % Examples: % -------- % % 1-D example % x = linspace(0,100,2^8); % y = cos(x/10)+(x/50).^2 + randn(size(x))/10; % y([70 75 80]) = [5.5 5 6]; % z = smoothn(y); % Regular smoothing % zr = smoothn(y,'robust'); % Robust smoothing % subplot(121), plot(x,y,'r.',x,z,'k','LineWidth',2) % axis square, title('Regular smoothing') % subplot(122), plot(x,y,'r.',x,zr,'k','LineWidth',2) % axis square, title('Robust smoothing') % % % 2-D example % xp = 0:.02:1; % [x,y] = meshgrid(xp); % f = exp(x+y) + sin((x-2*y)*3); % fn = f + randn(size(f))*0.5; % fs = smoothn(fn); % subplot(121), surf(xp,xp,fn), zlim([0 8]), axis square % subplot(122), surf(xp,xp,fs), zlim([0 8]), axis square % % % 2-D example with missing data % n = 256; % y0 = peaks(n); % y = y0 + rand(size(y0))*2; % I = randperm(n^2); % y(I(1:n^2*0.5)) = NaN; % lose 1/2 of data % y(40:90,140:190) = NaN; % create a hole % z = smoothn(y); % smooth data % subplot(2,2,1:2), imagesc(y), axis equal off % title('Noisy corrupt data') % subplot(223), imagesc(z), axis equal off % title('Recovered data ...') % subplot(224), imagesc(y0), axis equal off % title('... compared with original data') % % % 3-D example % [x,y,z] = meshgrid(-2:.2:2); % xslice = [-0.8,1]; yslice = 2; zslice = [-2,0]; % vn = x.*exp(-x.^2-y.^2-z.^2) + randn(size(x))*0.06; % subplot(121), slice(x,y,z,vn,xslice,yslice,zslice,'cubic') % title('Noisy data') % v = smoothn(vn); % subplot(122), slice(x,y,z,v,xslice,yslice,zslice,'cubic') % title('Smoothed data') % % % Cardioid % t = linspace(0,2*pi,1000); % x = 2*cos(t).*(1-cos(t)) + randn(size(t))*0.1; % y = 2*sin(t).*(1-cos(t)) + randn(size(t))*0.1; % z = smoothn(complex(x,y)); % plot(x,y,'r.',real(z),imag(z),'k','linewidth',2) % axis equal tight % % % Cellular vortical flow % [x,y] = meshgrid(linspace(0,1,24)); % Vx = cos(2*pi*x+pi/2).*cos(2*pi*y); % Vy = sin(2*pi*x+pi/2).*sin(2*pi*y); % Vx = Vx + sqrt(0.05)*randn(24,24); % adding Gaussian noise % Vy = Vy + sqrt(0.05)*randn(24,24); % adding Gaussian noise % I = randperm(numel(Vx)); % Vx(I(1:30)) = (rand(30,1)-0.5)*5; % adding outliers % Vy(I(1:30)) = (rand(30,1)-0.5)*5; % adding outliers % Vx(I(31:60)) = NaN; % missing values % Vy(I(31:60)) = NaN; % missing values % Vs = smoothn(complex(Vx,Vy),'robust'); % automatic smoothing % subplot(121), quiver(x,y,Vx,Vy,2.5), axis square % title('Noisy velocity field') % subplot(122), quiver(x,y,real(Vs),imag(Vs)), axis square % title('Smoothed velocity field') % % See also SMOOTH, SMOOTH3, DCTN, IDCTN. % % -- Damien Garcia -- 2009/03, revised 2010/11 % Visit my <a % href="matlab:web('http://www.biomecardio.com/matlab/smoothn.html')">website</a> for more details about SMOOTHN % Check input arguments error(nargchk(1,12,nargin)); %% Test & prepare the variables %--- k = 0; while k<nargin && ~ischar(varargin{k+1}), k = k+1; end %--- % y = array to be smoothed y = double(varargin{1}); sizy = size(y); noe = prod(sizy); % number of elements if noe<2, z = y; return, end %--- % Smoothness parameter and weights W = ones(sizy); s = []; if k==2 if isempty(varargin{2}) || isscalar(varargin{2}) % smoothn(y,s) s = varargin{2}; % smoothness parameter else % smoothn(y,W) W = varargin{2}; % weight array end elseif k==3 % smoothn(y,W,s) W = varargin{2}; % weight array s = varargin{3}; % smoothness parameter end if ~isequal(size(W),sizy) error('MATLAB:smoothn:SizeMismatch',... 'Arrays for data and weights must have same size.') elseif ~isempty(s) && (~isscalar(s) || s<0) error('MATLAB:smoothn:IncorrectSmoothingParameter',... 'The smoothing parameter must be a scalar >=0') end %--- % "Maximal number of iterations" criterion I = find(strcmpi(varargin,'MaxIter'),1); if isempty(I) MaxIter = 100; % default value for MaxIter else try MaxIter = varargin{I+1}; catch ME error('MATLAB:smoothn:IncorrectMaxIter',... 'MaxIter must be an integer >=1') end if ~isnumeric(MaxIter) || ~isscalar(MaxIter) ||... MaxIter<1 || MaxIter~=round(MaxIter) error('MATLAB:smoothn:IncorrectMaxIter',... 'MaxIter must be an integer >=1') end end %--- % "Tolerance on smoothed output" criterion I = find(strcmpi(varargin,'TolZ'),1); if isempty(I) TolZ = 1e-3; % default value for TolZ else try TolZ = varargin{I+1}; catch ME error('MATLAB:smoothn:IncorrectTolZ',... 'TolZ must be in ]0,1[') end if ~isnumeric(TolZ) || ~isscalar(TolZ) || TolZ<=0 || TolZ>=1 error('MATLAB:smoothn:IncorrectTolZ',... 'TolZ must be in ]0,1[') end end %--- % "Initial Guess" criterion I = find(strcmpi(varargin,'Initial'),1); if isempty(I) isinitial = false; % default value for TolZ else isinitial = true; try z0 = varargin{I+1}; catch ME error('MATLAB:smoothn:IncorrectInitialGuess',... 'Z0 must be a