SLIMpy Tutorials

This page contains the SLIMpy Tutorials found in the ROOT/doc/tut/ directory

Example Set 1

This examples is for the SLIMpy beginer. We will build up to solving the l1 minimization problem. We denote y a seismic trace corrupted by swell noise. A possible approach to denoising takes advantage of the sparsity of swell noise in the DCT domain and of seismic signal in the wavelet domain. The forward problem is as follows:

$\textbf{y} = \left[ \begin{array}{ccc} \textbf{PC} & \vline & \textbf{W} \end{array}\right] \left[ \begin{array}{c} x_1 \\ \vdots \\ x_N \\ \hline x_{N+1} \\ \vdots \\ x_{2N} \end{array}\right]$

In this equation, $\left[ \begin{array}{ccc} x_1 & \ldots & x_N \end{array}\right]^T$ represents the DCT contribution in the total data and $\left[ \begin{array}{ccc} x_{N+1} & \ldots & x_{2N} \end{array}\right]^T$ the wavelet contribution. The operators $\textbf{P}$ , $\textbf{C}$ , and $\textbf{W}$ are a frequency weighting, the DCT, and the wavelet transforms, respectively. The inverse problem is as follows:

$\tilde{\textbf{x}} = \arg\min \|\textbf{x}\|_1\quad\mbox{s.t.}\quad\left[ \begin{array}{ccc} \textbf{PC} & \vline & \textbf{W} \end{array}\right]\textbf{x}=\textbf{y}$

and the denoise signal, s , is given by

$\textbf{s} = \textbf{W} \left[ \begin{array}{c} \tilde{x}_{N+1} \\ \vdots \\ \tilde{x}_{2N} \end{array}\right].$

Learing objectives:

To start a simple slimpy script.
Learn about SLIMpy.
Create a black box package to solve a general problem

Inputs:

swellnoise.rsf the synthetic model of the swell noise
sig.rsf the synthetic model of the data
data.rsf the synthetic model produced from sfsigmoid

Outputs:

esig.rsf the esimated signal
enoise.rsf the esimated noise
residual.rsf the diffrence between the data, esimated signal and esimated noise

Prerequisite:

SLIMpy and ContribSLIMpy
Madagascar
SCons
All steps require `scons' to be run from the Set1 directory to create inputs.

Integrate a new Linear Operator

Link: ExampleSet2

This examples is for a SLIMpy user who is familiar with the SLIMpy vector and linear operator API. In this example I will go through the steps to create a new linear operator in SLIMpy.

Learing objectives:

Add a new Linear Operator to SLIMpy
Gain more understanding about SLIMpy's AST

Inputs:

None so far

Python Modules:

new_fft_slimpy.py contains a slimpy fft linear operator
new_fft_rsf_integration.py contains the rsf definition of the fft operator

Outputs:

None so far

Prerequisite:

SLIMpy and ContribSLIMpy
Madagascar
SCons