压缩采样匹配追踪(CoSaMP)

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压缩感知重构算法之压缩采样匹配追踪(CoSaMP)
具体可参考：

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具体的MATLAB函数代码见附件：

1. clc,clear
   
2. % -- Measurement matrix "A"
   
3. N   = 2^10;
   
4. M   = round(N/2);
   
5. randn('state',239234);
   
6. rand( 'state',239234);
   
7. A   = randn(M,N)/sqrt(M);
   
8. 
   
9. % -- Sparse signal "x"
   
10. K   = round(M/5);
    
11. T   = randperm(N);
    
12. T   = T(1:K);
    
13. x   = zeros(N,1);
    
14. x(T)= randn(K,1);
    
15. 
    
16. %% Add some noise:
    
17. 
    
18. NOISE_LEVEL = 3;  % choose
    
19. 
    
20. b   = A*x;
    
21. randn('state',94350);
    
22. switch NOISE_LEVEL
    
23.     case 1
    
24.         sigma   = 0;              % noiseless
    
25.         disp('-------- Noiseless setting ----------');
    
26.     case 2
    
27.         sigma   = .3*norm(b)/sqrt(M); % noisy
    
28.         disp('-------- Noisy setting --------------');
    
29.     case 3
    
30.         sigma   = .9*norm(b)/sqrt(M); % extremely noisy
    
31.         disp('-------- Very noisy setting ---------');
    
32. end
    
33. z   = sigma*randn(M,1);
    
34. b   = b + z;
    
35. 
    
36. 
    
37. opts            = [];
    
38. opts.maxiter    = 50;
    
39. opts.tol        = 1e-8;
    
40. opts.HSS        = true;
    
41. opts.two_solves = true; % this can help, but no longer always works "perfectly" on noiseless data
    
42. opts.printEvery = 10;
    
43. % K_target    = round(length(b)/3)-1; opts.normTol = 2.0;
    
44. K_target        = 50;   % When extremely noisy, this is best; when no noise, this is sub-optimal
    
45. if sigma == 0
    
46. %     K_target        = 100;  % This doesn't work "perfectly" but is OK
    
47. %     K_target        = 102;  % This works "perfectly" with noiseless data
    
48.     K_target        = 150;  % Slower, but works "perfectly" with noiseless data
    
49. end
    
50. 
    
51. % opts.addK       = 2*K_target; % default
    
52. opts.addK       = K_target; % this seems to work a bit better
    
53. % opts.addK       = 5;    % make this smaller and CoSaMP behaves more like OMP
    
54.                         % (and does better for the correlated measurement matrix)
    
55. 
    
56. % opts.support_tol    = 1e-2;
    
57. fprintf('CoSaMP, -------------------------------\n\n');
    
58. [xk] = CoSaMP( A, b, K_target, [], opts);
    
59. fprintf('Error is %.2e\t\n\n', norm(xk-x)/norm(x));
    

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