what are the advantages and disadvantages of Matching Pursuit Algorithms for Sparse Approximation? and if there are alternative method better than Matching Pursuit
No security and certainty at both ends above in which are cured and those who die .
To my knowledge, the result depends on the atoms in your dictionary. Hence if you do not have atoms that fit your problem well, you will converge to a really bad solution. It also depends on what you would like to approximate. Short time series can work quite well, but if your data is quite large, performing an atom decomposition can be very time consuming. All in all, it depends on the data you want to approximate.
On the plus side, it is quite easy to code up, for instance have a look at the LASSO algorithm.
There is also the option of Basis Pursuit, which is a more general approach and optimizes the L1 norm instead of L2. I just read the original paper and it sounded quite good, but I did not follow up on how well it performs compared with MP.
Hope it helps.
Cheers
The advantages of OMP and MP algorithms for Direction of Arrival estimation:
Applying BS algorithms to a DOA problem enhances resolution
and decreases complexity. Moreover, the knowledge of the number
of signal sources is not required to know in these algorithms. In
addition, they do not need any post-processing to converge to
the ML solution since the output of these algorithms is straightly
the DOAs. ML algorithm compares all feasible directions and then
selects the most likely one. On the other hand, BS algorithms
compare some of the angles and select them in a smart method.
Hence, BS algorithms are much more computationally efficient
in comparison to other algorithms of DOA estimation such as
MUSIC and ESPRIT to approach to the ML solution. Moreover, BS
algorithms converge to the ML solution when the value of SNR
is low, whereas other approaches converge at high SNRs only.
In addition, in other methods for DOA estimation, the number
of estimated DOAs is limited by the number of antennas. The BS
based DOA estimation methods can estimate more DOAs than the
antennas number. Among BS methods, OMP algorithm provides
slightly higher performance than MP algorithm with moderately
higher computational complexity.
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