RILT fmincon

Compute the Regularized Inverse Laplace Transform of an autocorrelation function with the fmincon function. Similar to CONTIN.

The purpose of these codes is to compute the Regularized Inserve Laplace Transform (RILT) of an autocorrelation function. This is an update of CONTIN (S.W.Provencher, 1982) that was encoded in Fortran.

A similar code has been written by Iari-Gabriel Marino (2022). rilt (https://www.mathworks.com/matlabcentral/fileexchange/6523-rilt).

But this former code was based on fminsearch.

Here, we use the fmincon function that is more suitable and faster.

We use a logarithmic scale but it can be easily changed to a linear one.

'Main_file' is the main file to compute the RILT, and all other files are called from this one.

'Alpha' is a weight on the constraint and you may change it according to your data.

'RILT_fmincon.m' takes around 1s to run with Ns = 200. The complexity cost is more than linear.

'rosenbrock.m' contains the function to minimize.

In 'Data_Folder' you can find a toy signal ('filename.mat') that was built with an AR(1) process.

This algorithm is limited to exponential-like decreasing ACFs but it can be adapted to other kinds of ACFs through the matrix 'A'.

A more general article around this topic is:

'A multiscale time-Laplace method to extract relaxation times from non-stationary dynamic light scattering signals' (2022). https://doi.org/10.1063/5.0088005

This work is provided by François Liénard, Eric Freyssingeas and Pierre Borgnat (ENS de Lyon).