Persistence 1D inc. Reconstruct1D  1.1
Finding extrema in one dimensional data, filtering them by persistence and reconstructing smooth functions
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Reconstruct1D for Persistence1D

Reconsturct1D is a class for reconstructing smooth functions based on persistence features in one dimensional data.

Persistent features can be used to reconstruct a C1 or C2 smooth function which is similar to the original data.

The class can be used with Matlab's built-in quadprog solver, but we recommend to use the MOSEK solvers package which is faster.

The class relies on Persistence1D main package and its output format.

Purpose

The class is used to reconstruct a smooth function which is similar to the input data. The reconstruction process guarantees:

Usage

To reconstruct a smooth function, the algorithm does the following:

  1. Use Persistence1d to find features
  2. Choose threshold for surviving features.
  3. Build equality, inequality and monotonicity constraints.
  4. Solve the optimization problems.

Interaction with Reconstruct1D can be done in two different ways:

The data about the location of persistent features is being used to create equality and inequality constraints for the entire data domain. The reconstructed function will have biharmonic or triharmonic solution, i.e. C1 or C2 smoothness.

Please check the Examples section and Reconstruct1D\Examples folder.

MOSEK Solvers

It is highly recommended to install and use MOSEK with this package, as Matlab's quadprog solver is slow. Download MOSEK [http://www.mosek.com/] and install it. It is possible to use it with a free academic license or with a trial license. Your Matlab installation, operating system and MOSEK architecture should all match.

Reconstruct1D includes two files to turn MOSEK on and off, but they might require adjustments based on your system settings.

turn_on_mosek - use this to turn on MOSEK optimizers before calling Reconstruct1d. Adds MOSEK to Matlab's path.

turn_off_mosek - turns off MOSEK solvers, be removing it from Matlab's path.

Before first use, open turn_on_mosek.m and turn_off_mosek.m to configure your MOSEK installation path.

Examples

Reconstruct1d\examples folder contains:

Functions

Interface Functions

reconstruct1d.m

reconstruct1d_with_persistence_res.m

setup_persistence1d.m

turn_off_mosek.m

turn_on_mosek.m

plot_reconstructed_data.m

Internal Functions

build_equality_constraints.m

build_inequality_constraints.m

build_laplacian.m

build_monotonicity_graph.m