Date: Sun, 29 May 2022 05:47:16 +0300 (EEST) Message-ID: <1083493130.8403.1653792436103@wiki-1.it.helsinki.fi> Subject: Exported From Confluence MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_Part_8402_54855003.1653792436103" ------=_Part_8402_54855003.1653792436103 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/exported.html 1D Deconvolution

# 1D Deconvolution

## One-dime= nsional deconvolution

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This page contains the computational Matlab files related to the book  Linear and Nonlinear Inverse Problems wit= h Practical Applications
written by Jennifer Mueller and Samul= i Siltanen and published by SIAM in 2012.

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You can order the book at the SIAM webshop.

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### Simulation of con= volution data

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You will need these files:

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These routines create and plot high-resolution convolution data:

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For practical purposes we need discrete and not so high-dimensional data= :

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You can try out naive deconvolution:

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DC3_naive_plot.m

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### Truncated SVD

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Here is a routine for recovering the original signal from convolution da= ta using truncated singular value decomposition. Note that the program paus= es after each plot and waits for you to press any key to continue. You can = see how the reconstruction changes when more singular vectors are used.

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DC4_truncSVD_comp.m

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### Tikhonov regularizatio= n

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In this routine you can use classical Tikhonov regularization for the de= convolution task. Try to change the regularization parameter and see what h= appens!

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DC5_Tikhonov_comp.m

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This file implements generalized Tikhonov regularization with derivative= penalty. Again, test the effect of changing the regularization parameter.<= /p>=20

DC6_TikhonovD_comp.m

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### Total variation = regularization

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Here we apply the total variation regularization to the deconvolution pr= oblem.

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DC7_TotalVariation_comp.m

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