Why OMP is iterative? Can we find the support in one step?

In summary, the 'support' of the received signal in OMP is not found in one step by simply selecting the $K$ maximum correlated columns of the sensing matrix $A$. Instead, it is found in an iterative fashion, where the $K$ most correlated columns are selected and added to the support set in each iteration until the desired sparsity level is reached. This is because more computation is needed at each iteration to find the optimal support set. For more details, please refer to the paper provided.
  • #1
Awais088
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In OMP why the 'support' of the received signal is not found in one step, by selecting the $K$ maximum correlated columns of the sensing matrix $A$? where $K$ is the sparsity of the signal. Like in MATLAB

[val ind] = sort(A'*Y); %Y is received signal
signal_Support = ind(1:K); % The result is almost the same as that of normal OMP

Why the support is found in an iterative fashion? As more computation is needed at each iteration.
 
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  • #2
Awais088 said:
In OMP why the 'support' of the received signal is not found in one step, by selecting the $K$ maximum correlated columns of the sensing matrix $A$? where $K$ is the sparsity of the signal. Like in MATLAB

[val ind] = sort(A'*Y); %Y is received signal
signal_Support = ind(1:K); % The result is almost the same as that of normal OMP

Why the support is found in an iterative fashion? As more computation is needed at each iteration.
Can you show us your computations in more detail now? Hopefully you've made some progress on this. See this paper for example:

https://pdfs.semanticscholar.org/425b/1a11936405eb4f8c93dafc33fcc1b485f2a5.pdf
:smile:
 

Why is OMP iterative?

OMP (Orthogonal Matching Pursuit) is an algorithm used for sparse signal recovery. It is iterative because it involves repeated iterations to find the best approximation of the sparse signal. This is necessary because the algorithm starts with an initial guess and then updates it with each iteration until the desired level of accuracy is achieved.

What is the purpose of iterations in OMP?

The purpose of iterations in OMP is to refine the estimated sparse signal. Each iteration involves selecting the most significant components of the signal and updating the approximation to better match the original signal. This process is repeated until the desired level of accuracy is achieved.

How many iterations are required in OMP?

The number of iterations required in OMP depends on the desired level of accuracy and the complexity of the signal. Generally, the more sparse the signal, the fewer iterations are required. However, there is no set number of iterations that applies to all cases. The algorithm will continue to iterate until the desired accuracy is achieved.

Can we find the support of the sparse signal in one step using OMP?

No, we cannot find the support of the sparse signal in one step using OMP. The algorithm requires multiple iterations to refine the estimated signal and identify the significant components. Attempting to find the support in one step would result in a less accurate approximation of the signal.

Is there a faster method to find the support of a sparse signal?

OMP is considered one of the fastest methods for finding the support of a sparse signal. However, there are other algorithms, such as LASSO and Basis Pursuit, that can also be used for this purpose. Each algorithm has its own advantages and disadvantages, so the best method may vary depending on the specific signal and application.

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