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How to threshold wavelet coefficients ( keep largest 1/2 of them )?

Posted 11 years ago

I am using Mathematica 9

I got

dwd = DiscreteWaveletTransform[data]

It returns a DiscreteWaveletData object with coefficients ( I assume ).

Now I want to keep only 1/2 largest, to the module , wavelet coefficients from dwd. How to do so?

Is there any way to use WaveletThreshold[] to do that?

Thank you in advance.

POSTED BY: Me Myself
3 Replies

I think Bill has provided very useful information to solve your problem. Following his suggestion, to achieve what you asked, WaveletThreshold looks like the function to do the task.

However, your question of keeping 1/2 largest is not clear to me at what indices and how to compute the threshold. Do you only want to threshold on all indices or detail ones? Is 1/2 largest meaning over all indices or just detail ones?

Once you have computed the threshold with the information Bill has provided, WaveletThreshold allows you to specify which index to perform the thresholding.

WaveletThreshold[ dwd, {"Hard", threshold}, indice]

For example, this code thresholds all indices:

SeedRandom[1];data = RandomReal[{-1, 1}, {8}];
dwd = DiscreteWaveletTransform[data];
Normal@WaveletThreshold[dwd, {"Hard", Median[Abs@Flatten[Last /@ Normal[dwd]]]}, All]

returns

   {{0} -> {0., 0., -0.979909, 0.}, {1} -> {0.998392, 0.850965, 0., 
   0.}, {0, 0} -> {0., -0.919499}, {0, 1} -> {0., -0.466301}, {0, 0, 
   0} -> {-0.716554}, {0, 0, 1} -> {0.583814}}
POSTED BY: MinHsuan Peng
Posted 11 years ago

If you want to peek at all the details really returned by DiscreteWaveletTransform then do this:

In[1]:= data = RandomReal[{-1, 1}, {8}];
Normal[DiscreteWaveletTransform[data]]

Out[2]= {{0}->{-0.0640216, 0.201553, 0.566641, 0.44696}, {1}->{-0.0263881, -0.110478, -0.650836, -0.449402},
  {0, 0}->{0.0972497, 0.716724}, {0, 1}->{-0.18779, 0.0846273}, {0, 0, 0}->{0.575566}, {0, 0, 1}->{-0.438034}}

Then on the help page for DiscreteWaveletTransform you can click on Details and Options and guess how to interpret this tree information you are given.

This might even help you see how to check to see whether the processing of the results turned out to be correct.

POSTED BY: Bill Simpson
Posted 10 years ago

Nice, but your answer dosen't seem to be related in any way to my problem. I have checked Details - no insight gained.

POSTED BY: me myself
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