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I read following paper. [2019, Emilie Chouzenoux, A Proximal Interior Point Algorithm with Applications to Image Processing]

Wavelet operator

The problem is constructed as Proximal interior point method, and solved by the proposed PIPA algorithm. In the objective function, as a regularization, they used Wavelet decomposition operator.

For using the algorithm Wavelet should be represented by linear operator. But I can't find how to represent wavelet decomposition as matrix-vector multiplication.

So could you recommend any reference or lectures? Thank you.

Jongkyu Lee
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1 Answers1

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There is some discussion here regarding example matrix operators for Haar wavelets: https://en.wikipedia.org/wiki/Haar_wavelet#Haar_matrix . Additionally, you may wish to consider the MIT open courseware Linear Algebra by Prof. Strang, in particular a lecture on image compression including wavelets: https://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/positive-definite-matrices-and-applications/change-of-basis-image-compression/.

I hope this helps.

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