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February 2015

# FLSA

Computing a graph induced Fused LASSO Signal Approximator. You can use it to denoise data. The package includes some utility methods to assess the algorithms and apply it to images as well es ion-mobilty spectrometry (IMS) data sets.

## Mathematical Formulation For the one dimensional version of the Johnson's dynamic programming algorithm, have a look into Lasso.jl

## Denoising

The fused LASSO signal approximator can be used to denoise e.g. images:

#### Noisy Input #### Cleaned by FLSA ## Algorithms

Also known as Fast Iterative Shrinkage Algorithm (FISTA).

### Maximum Gap Tree (MGT)

Own algorithm based on a iterative approximation by dynamic programming algorithm minimizing a sub-tree-graph.

## Example

### Image Graph

```using FLSA
graph = FLSA.img_graph(size(B)..., dn=2, lam=0.1)   # (1)
F = FLSA.fista(B, graph, verbose=true; max_iter=10) # (2)```

First you have to define graph (line `(1)`). Then one of the algorithms above are called (see `(2)`).

### HDF5 Input

In order to be easily called from other languages a HDF5 intermediate data structure is supported that looks as follows (see generate_hdf5.py for a working python example):

``````             1 2 3 ... n
nodes/input
/weight

1 2 3 ... m