## 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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Go to master p=
age

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### Simulation of con=
volution data

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You will need these files:

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DC_PSF.m,=
DC_t=
arget.m, DC_convmtx.m.

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These routines create and plot high-resolution convolution data:

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DC1_cont_data_comp.m, DC1_cont_data_plot.m=
.

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

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DC2_discretedata_comp.m, DC2_discre=
tedata_plot.m.

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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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