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I have a matrix whose columns are highly correlated, hence using this matrix in compressed sensing algorithms is not giving satisfactory results. So is there any way in which we can reduce the linear dependency between the columns of the matrix?

Snapshots of measurement vector 'y', sensing matrix'A' and required solution vector'x' are attachedmeasurement vector

Sensing matrix Solution vector (nearly sparse)

Anurag Das
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    Would principal component analysis (“PCA”) do the trick? – Dave Dec 12 '19 at 05:08
  • How to use PCA for this? Basically the columns are highly correlated hence they will be oriented along the single principal direction. – Anurag Das Dec 12 '19 at 05:24
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    PCA functions on correlated data to de-correlate the data and give mutually orthogonal directions. – Dave Dec 12 '19 at 05:28
  • Thanks Dave, can you share link on where to read more about this. – Anurag Das Dec 12 '19 at 05:35
  • Suppose I have ave a matrix A=[1 2; 2 4]can the columns be decorrelated using PCA? – Anurag Das Dec 12 '19 at 05:37
  • @AnuragDas please provide more details as to what you are doing, and sharing a small snapshot of data may help too. Is it your matrix square or rectangular? Are you allowed to drop some variables? What are your exact objectives? – PsychometStats Dec 12 '19 at 12:09
  • Here's your link: https://stats.stackexchange.com/questions/tagged/pca?tab=Votes. – whuber Dec 12 '19 at 17:06
  • @PsychometStats I am using compressed sensing to recover my sparse solution vector 'x' from a given sensing matrix 'A' which is rectangular and measurement vector 'y'. Since the columns of 'A' are highly co-related I want to know whether by any means I can reduce the linear dependancy between the columns such that compressive sensing algotithms can be applied to give satisfactory results. – Anurag Das Dec 13 '19 at 05:05
  • @PsychometStats I have attaches snapshots to my answer. – Anurag Das Dec 13 '19 at 05:12

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