## [2f5a82]: frames / franagrouplasso.m  Maximize  Restore  History

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179``` ```function [tc,relres,iter,xrec] = franagrouplasso(F,insig,lambda,varargin) %FRANAGROUPLASSO Group LASSO regression in the TF-domain % Usage: [tc,xrec] = franagrouplasso(F,x,group,lambda,C,maxit,tol) % % Input parameters: % F : Frame definition % x : Input signal % lambda : Regularization parameter, controls sparsity of the % solution % Output parameters: % tc : Thresholded coefficients % relres : Vector of residuals. % iter : Number of iterations done. % xrec : Reconstructed signal % % `franagrouplasso(F,x)` solves the group LASSO regression problem in the % time-frequency domain: minimize a functional of the synthesis % coefficients defined as the sum of half the \$l^2\$ norm of the % approximation error and the mixed \$l^1\$ / \$l^2\$ norm of the coefficient % sequence, with a penalization coefficient lambda. % % The matrix of time-frequency coefficients is labelled in terms of groups % and members. By default, the obtained expansion is sparse in terms of % groups, no sparsity being imposed to the members of a given group. This % is achieved by a regularization term composed of \$l^2\$ norm within a % group, and \$l^1\$ norm with respect to groups. See the help on % |groupthresh| for more information. % % `[tc,relres,iter] = franagrouplasso(...)` returns the residuals *relres* in % a vector and the number of iteration steps done, *maxit*. % % `[tc,relres,iter,xrec] = franagrouplasso(...)` returns the reconstructed % signal from the coefficients, *xrec*. Note that this requires additional % computations. % % The function takes the following optional parameters at the end of % the line of input arguments: % % 'freq' Group in frequency (search for tonal components). This is the % default. % % 'time' Group in time (search for transient components). % % 'C',cval Landweber iteration parameter: must be larger than % square of upper frame bound. Default value is the upper % frame bound. % % 'maxit',maxit % Stopping criterion: maximal number of iterations. % Default value is 100. % % 'tol',tol Stopping criterion: minimum relative difference between % norms in two consecutive iterations. Default value is % 1e-2. % % 'print' Display the progress. % % 'quiet' Don't print anything, this is the default. % % 'printstep',p % If 'print' is specified, then print every p'th % iteration. Default value is 10; % % In addition to these parameters, this function accepts all flags from % the |groupthresh| and |thresh| functions. This makes it possible to % switch the grouping mechanism or inner thresholding type. % % The parameters *C*, *maxit* and *tol* may also be specified on the % command line in that order: `franagrouplasso(F,x,lambda,C,tol,maxit)`. % % The solution is obtained via an iterative procedure, called Landweber % iteration, involving iterative group thresholdings. % % The relationship between the output coefficients is given by :: % % xrec = frsyn(F,tc); % % See also: franalasso, framebounds % % References: Kowalski08sparsity kowalski2009mixed if nargin<2 error('%s: Too few input parameters.',upper(mfilename)); end; if ~isvector(insig) error('Input signal must be a vector.'); end % Define initial value for flags and key/value pairs. definput.import={'thresh','groupthresh'}; definput.flags.group={'freq','time'}; definput.keyvals.C=[]; definput.keyvals.maxit=100; definput.keyvals.tol=1e-2; definput.keyvals.printstep=10; definput.flags.print={'quiet','print'}; [flags,kv]=ltfatarghelper({'C','tol','maxit'},definput,varargin); L=framelength(F,length(insig)); F=frameaccel(F,L); if isempty(kv.C) [~,kv.C] = framebounds(F,L); end; % Initialization of thresholded coefficients c0 = frana(F,insig); % We have to convert the coefficients to time-frequency layout to % discover their size tc = framecoef2tf(F,c0); [M,N]=size(tc); % Normalization to turn lambda to a value comparable to lasso %if flags.do_time % lambda = lambda*sqrt(N); %else % lambda = lambda*sqrt(M); %end % Various parameter initializations threshold = lambda/kv.C; tc0 = c0; relres = 1e16; iter = 0; % Choose the dimension to group along if flags.do_freq kv.dim=2; else kv.dim=1; end; if F.red==1 tc=groupthresh(tc,threshold,kv.dim,flags.iofun); % Convert back from TF-plane tc=frametf2coef(F,tc); else % Main loop while ((iter < kv.maxit)&&(relres >= kv.tol)) tc = c0 - frana(F,frsyn(F,tc0)); tc = tc0 + tc/kv.C; % ------------ Convert to TF-plane --------- tc = framecoef2tf(F,tc); tc = groupthresh(tc,threshold,'argimport',flags,kv); % Convert back from TF-plane tc=frametf2coef(F,tc); % ------------------------------------------- relres = norm(tc(:)-tc0(:))/norm(tc0(:)); tc0 = tc; iter = iter + 1; if flags.do_print if mod(iter,kv.printstep)==0 fprintf('Iteration %d: relative error = %f\n',iter,relres); end; end; end end; % Reconstruction if nargout>3 xrec = frsyn(F,tc); end; ```