function Result = BSBL_BO(Phi, y, blkStartLoc, LearnLambda, varargin)
% BSBL-BO: Recover block sparse signal (1D) exploiting intra-block correlation, given the block partition.
%
% The algorithm solves the inverse problem for the block sparse
% model with known block partition:
% y = Phi * x + v
%
%
% ============================== INPUTS ==============================
% Phi : N X M known matrix
%
% y : N X 1 measurement vector
%
% blkStartLoc : Start location of each block
%
% LearnLambda : (1) If LearnLambda = 1, use the lambda learning rule for very LOW SNR cases (SNR<10dB)
% (using lambda=std(y)*1e-2 or user-input value as initial value)
% (2) If LearnLambda = 2, use the lambda learning rule for medium noisy cases (SNR>10dB)
% (using lambda=std(y)*1e-2 or user-input value as initial value)
% (3) If LearnLambda = 0, do not use the lambda learning rule
% ((using lambda=1e-14 or user-input value as initial value)
%
%
% [varargin values -- in most cases you can use the default values]
%
% 'LEARNTYPE' : LEARNTYPE = 0: Ignore intra-block correlation
% LEARNTYPE = 1: Exploit intra-block correlation
% [ Default: LEARNTYPE = 1 ]
%
% 'PRUNE_GAMMA' : threshold to prune out small gamma_i
% (generally, 10^{-3} or 10^{-2})
%
% 'LAMBDA' : user-input value for lambda
% [ Default: LAMBDA=1e-14 when LearnLambda=0; LAMBDA=std(y)*1e-2 in noisy cases]
%
% 'MAX_ITERS' : Maximum number of iterations.
% [ Default value: MAX_ITERS = 600 ]
%
% 'EPSILON' : Solution accurancy tolerance parameter
% [ Default value: EPSILON = 1e-8 ]
%
% 'PRINT' : Display flag. If = 1: show output; If = 0: supress output
% [ Default value: PRINT = 0 ]
%
% ============================== OUTPUTS ==============================
% Result :
% Result.x : the estimated block sparse signal
% Result.gamma_used : indexes of nonzero groups in the sparse signal
% Result.gamma_est : the gamma values of all the groups of the signal
% Result.B : the final value of the B
% Result.count : iteration times
% Result.lambda : the final value of lambda
%
%
% ========================= Command examples =============================
% < Often-used command >
% For most noisy environment (SNR > 10dB):
%
% Result = BSBL_BO(Phi, y, blkStartLoc, 2);
%
% For very low SNR cases (SNR < 10 dB):
%
% Result = BSBL_BO(Phi, y, blkStartLoc, 1);
%
% For noiseless cases:
%
% Result = BSBL_BO(Phi, y, blkStartLoc, 0);
%
% To recover non-Sparse structured signals (noiseless):
% Result = BSBL_BO(Phi,y,groupStartLoc,0,'prune_gamma',-1);
% ('prune_gamma' can be set any non positive constant)
%
% < Full-Command Example >
% Result = BSBL_BO(Phi, y, blkStartLoc, learnlambda, ...
% 'LEARNTYPE', 1,...
% 'PRUNE_GAMMA',1e-2,...
% 'LAMBDA',1e-3,...
% 'MAX_ITERS', 800,...
% 'EPSILON', 1e-8,...
% 'PRINT',0);
%
% ================================= See Also =============================
% EBSBL_BO, BSBL_EM, BSBL_L1, EBSBL_L1, TMSBL, TSBL
%
% ================================ Reference =============================
% [1] Zhilin Zhang, Bhaskar D. Rao, Extension of SBL Algorithms for the
% Recovery of Block Sparse Signals with Intra-Block Correlation,
% available at: http://arxiv.org/abs/1201.0862
%
% [2] Zhilin Zhang, Tzyy-Ping Jung, Scott Makeig, Bhaskar D. Rao,
% Low Energy Wireless Body-Area Networks for Fetal ECG Telemonitoring
% via the Framework of Block Sparse Bayesian Learning,
% available at: http://arxiv.org/pdf/1205.1287v1.pdf
%
% [3] webpage: http://dsp.ucsd.edu/~zhilin/BSBL.html, or
% https://sites.google.com/site/researchbyzhang/bsbl
%
% ============= Author =============
% Zhilin Zhang (z4zhang@ucsd.edu, zhangzlacademy@gmail.com)
%
% ============= Version =============
% 1.4 (07/23/2012) debug
% 1.3 (05/30/2012) make faster
% 1.2 (05/28/2012)
% 1.1 (01/22/2012)
% 1.0 (08/27/2011)
%
% scaling...
scl = std(y);
if (scl < 0.4) | (scl > 1)
y = y/scl*0.4;
end
% Default Parameter Values for Any Cases
EPSILON = 1e-8; % solution accurancy tolerance
MAX_ITERS = 600; % maximum iterations
PRINT = 0; % don't show progress information
LEARNTYPE = 1; % adaptively estimate the covariance matrix B
if LearnLambda == 0
lambda = 1e-12;
PRUNE_GAMMA = 1e-3;
elseif LearnLambda == 2
lambda = scl * 1e-2;
PRUNE_GAMMA = 1e-2;
elseif LearnLambda == 1
lambda = scl * 1e-2;
PRUNE_GAMMA = 1e-2;
else
error(['Unrecognized Value for Input Argument ''LearnLambda''']);
end
if(mod(length(varargin),2)==1)
error('Optional parameters should always go by pairs\n');
else
for i=1:2:(length(varargin)-1)
switch lower(varargin{i})
case 'learntype'
LEARNTYPE = varargin{i+1};
if LEARNTYPE ~= 1 & LEARNTYPE ~= 0
error(['Unrecognized Value for Input Argument ''LEARNTYPE''']);
end
case 'prune_gamma'
PRUNE_GAMMA = varargin{i+1};
case 'lambda'
lambda = varargin{i+1};
case 'epsilon'
EPSILON = varargin{i+1};
case 'print'
PRINT = varargin{i+1};
case 'max_iters'
MAX_ITERS = varargin{i+1};
otherwise
error(['Unrecognized parameter: ''' varargin{i} '''']);
end
end
end
if PRINT
fprintf('\n====================================================\n');
fprintf(' Running BSBL-BO ....... \n');
fprintf(' Information about parameters...\n');
fprintf('====================================================\n');
fprintf('PRUNE_GAMMA : %e\n',PRUNE_GAMMA);
fprintf('lambda : %e\n',lambda);
fprintf('LearnLambda : %d\n',LearnLambda);
fprintf('LearnType : %d\n',LEARNTYPE);
fprintf('EPSILON : %e\n',EPSILON);
fprintf('MAX_ITERS : %d\n\n',MAX_ITERS);
end
%% Initialization
[N,M] = size(Phi);
Phi0 = Phi;
blkStartLoc0 = blkStartLoc;
p = length(blkStartLoc); % block number
for k = 1 : p-1
blkLenList(k) = blkStartLoc(k+1)-blkStartLoc(k);
end
blkLenList(p) = M - blkStartLoc(end)+1;
maxLen = max(blkLenList);
if sum(blkLenList == maxLen) == p,
equalSize = 1;
else
equalSize = 0;
end
for k = 1 : p
Sigma0{k} = eye(blkLenList(k));
end
gamma = ones(p,1);
keep_list = [1:p]';
usedNum = length(keep_list);
mu_x = zeros(M,1);
count = 0;
%% Iteration
while (1)
count = count + 1;
%=========== Prune weighys as yheir hyperparameyers go yo zero ==============
if (min(gamma) < PRUNE_GAMMA)
index = find(gamma > PRUNE_GAMMA);
usedNum = length(index);
keep_list = keep_list(index);
if isempty(keep_list),
fprintf('\n====================================================================================\n');
fprintf('x becomes zero vector. The solution may be incorrect. \n');
fpr
