1.matlab 没有wavefast函数,源码怎么回事,我是2012a
2.Matlab实现小波变换
matlab 没有wavefast函数,怎么回事,我是2012a
function [c, s] = wavefast(x, n, varargin)
%WAVEFAST Perform multi-level 2-dimensional fast wavelet transform.
% [C, L] = WAVEFAST(X, N, LP, HP) performs a 2D N-level FWT of
% image (or matrix) X with respect to decomposition filters LP and
% HP.
%
% [C, L] = WAVEFAST(X, N, WNAME) performs the same operation but
% fetches filters LP and HP for wavelet WNAME using WAVEFILTER.
%
% Scale parameter N must be less than or equal to log2 of the
% maximum image dimension. Filters LP and HP must be even. To
% reduce border distortion, X is symmetrically extended. That is,
% if X = [c1 c2 c3 ... cn] (in 1D), then its symmetric extension
% would be [... c3 c2 c1 c1 c2 c3 ... cn cn cn-1 cn-2 ...].
%
% OUTPUTS:
% Matrix C is a coefficient decomposition vector:
%
% C = [ a(n) h(n) v(n) d(n) h(n-1) ... v(1) d(1) ]
%
% where a, h, v, and d are columnwise vectors containing
% approximation, horizontal, vertical, and diagonal coefficient
% matrices, respectively. C has 3n + 1 sections where n is the
% number of wavelet decompositions.
%
% Matrix S is an (n+2) x 2 bookkeeping matrix:
%
% S = [ sa(n, :); sd(n, :); sd(n-1, :); ... ; sd(1, :); sx ]
%
% where sa and sd are approximation and detail size entries.
%
% See also WAVEBACK and WAVEFILTER.
% Copyright - R. C. Gonzalez, R. E. Woods, & S. L. Eddins
% Digital Image Processing Using MATLAB, Prentice-Hall,
% $Revision: 1.5 $ $Date: // :: $
% Check the input arguments for reasonableness.
error(nargchk(3, 4, nargin));
if nargin == 3
if ischar(varargin{ 1})
[lp, hp] = wavefilter(varargin{ 1}, 'd');
else
error('Missing wavelet name.');
end
else
lp = varargin{ 1}; hp = varargin{ 2};
end
fl = length(lp); sx = size(x);
if (ndims(x) ~= 2) | (min(sx) < 2) | ~isreal(x) | ~isnumeric(x)
error('X must be a real, numeric matrix.');
end
if (ndims(lp) ~= 2) | ~isreal(lp) | ~isnumeric(lp) ...
| (ndims(hp) ~= 2) | ~isreal(hp) | ~isnumeric(hp) ...
| (fl ~= length(hp)) | rem(fl, 2) ~= 0
error(['LP and HP must be even and equal length real, ' ...
'numeric filter vectors.']);
end
if ~isreal(n) | ~isnumeric(n) | (n < 1) | (n > log2(max(sx)))
error(['N must be a real scalar between 1 and ' ...
'log2(max(size((X))).']);
end
% Init the starting output data structures and initial approximation.
c = []; s = sx; app = double(x);
% For each decomposition ...
for i = 1:n
% Extend the approximation symmetrically.
[app, keep] = symextend(app, fl);
% Convolve rows with HP and downsample. Then convolve columns
% with HP and LP to get the diagonal and vertical coefficients.
rows = symconv(app, hp, 'row', fl, keep);
coefs = symconv(rows, hp, 'col', fl, keep);
c = [coefs(:)' c]; s = [size(coefs); s];
coefs = symconv(rows, lp, 'col', fl, keep);
c = [coefs(:)' c];
% Convolve rows with LP and downsample. Then convolve columns
% with HP and LP to get the horizontal and next approximation
% coeffcients.
rows = symconv(app, lp, 'row', fl, keep);
coefs = symconv(rows, hp, 'col', fl, keep);
c = [coefs(:)' c];
app = symconv(rows, lp, 'col', fl, keep);
end
% Append final approximation structures.
c = [app(:)' c]; s = [size(app); s];
%-------------------------------------------------------------------%
function [y, keep] = symextend(x, fl)
% Compute the number of coefficients to keep after convolution
% and downsampling. Then extend x in both dimensions.
keep = floor((fl + size(x) - 1) / 2);
y = padarray(x, [(fl - 1) (fl - 1)], 'symmetric', 'both');
%-------------------------------------------------------------------%
function y = symconv(x, h, type, fl, keep)
% Convolve the rows or columns of x with h, downsample,
% and extract the center section since symmetrically extended.
if strcmp(type, 'row')
y = conv2(x, h);
y = y(:, 1:2:end);
y = y(:, fl / 2 + 1:fl / 2 + keep(2));
else
y = conv2(x, h');
y = y(1:2:end, :);
y = y(fl / 2 + 1:fl / 2 + keep(1), :);
end
Matlab实现小波变换
实现小波变换的MATLAB操作涉及到一系列关键步骤与函数，包括使用Haar滤波器进行简单FWT（离散小波变换），源码比较函数wavefast和wavedec2的源码执行时间，以及探索小波的源码axel ftp源码方向性和边缘检测能力。
首先，源码使用Haar滤波器作为基本工具，源码foursquare源码MATLAB中的源码小波函数提供了一种简便的执行方法。通过调用这些函数，源码用户可以对图像或信号进行离散小波变换，源码实现数据的源码多分辨率分析。
对比函数wavefast和wavedec2的源码性能表现，用户可利用MATLAB的源码内置功能评估不同算法的效率和精确度。这种比较有助于在实际应用中选择最适合特定任务的源码filechannelimpl 源码算法。
探索小波的源码方向性，是源码深入理解其在边缘检测等应用中优势的关键。MATLAB提供了丰富的codeproject 源码工具和函数，如小波包分析等，用户可以使用这些工具来分析和处理不同方向的边缘信息，从而提高图像处理的koreeasy源码精度和效果。
参考文献为了解小波变换的理论基础与应用提供了重要资源，包括Rafael C. Gonzalez, Richard E. Woods, and Steven L. Eddins的《Digital Image Processing Using MATLAB》、阮秋琦的《数字图像处理（MATLAB版）》、以及冈萨雷斯的《数字图像处理（第三版）》。这些文献不仅提供了理论知识，还包含了许多实用的MATLAB代码示例。
为了获取文章和代码等相关资源，用户可以访问Github仓库： digital-image-processing-matlab，或者通过公众号AIShareLab回复“数字图像处理”获取资源。