tut/Set1/SConstruct

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"""/*!
@page ExampleSet1 Example Set 1

 This examples is for the SLIMpy beginer.
 We will build up to solving the l1 minimization problem.
 We denote @b 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:
 
   \f[
  \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]
   \f]
   
In this equation, \f$\left[
  \begin{array}{ccc}
    x_1 & \ldots & x_N
  \end{array}\right]^T
\f$ represents the DCT contribution in the total data and \f$\left[
  \begin{array}{ccc}
    x_{N+1} & \ldots & x_{2N}
  \end{array}\right]^T
\f$ the wavelet contribution. The operators @f$\textbf{P}@f$, @f$\textbf{C}@f$,
and @f$\textbf{W}@f$ are a frequency weighting, the DCT, and the wavelet
transforms, respectively. The inverse problem is as follows:

\f[
  \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}

\f]
and the denoise signal, @b s , is given by

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

   \par Learing objectives:
     - To start a simple slimpy script.  
     - Learn about SLIMpy.
     - Create a black box package to solve a general problem

\par Inputs:
 - \a swellnoise.rsf the synthetic model of the swell noise
 - \a sig.rsf the synthetic model of the data
 - \a data.rsf the synthetic model produced from sfsigmoid
\par Outputs:
 - \a esig.rsf the esimated signal 
 - \a enoise.rsf the esimated noise
 - \a residual.rsf the diffrence between the data, esimated signal and esimated noise
\par Prerequisite:
 - SLIMpy and ContribSLIMpy
 - Madagascar
 - SCons
 - All steps require `scons' to be run from the Set1 directory to create inputs.

@section s1 Step 1
Link: @subpage es1step1 
@copydoc es1step1

@section s2 Step 2
Link: @subpage es1step2 
@copydoc es1step2

@section s3 Step 3
Link: @subpage es1step3 
@copydoc es1step3

@section s4 Step 4
Link: @subpage es1step4 
@copydoc es1step4

@section s5 Step 5
Link: @subpage es1step5 
@copydoc es1step5

@section s6 Step 6
Link: @subpage es1step6 
@copydoc es1step6

@section s7 Step 7
Link: @subpage es1step7 
@copydoc es1step7

*/"""


from rsfproj import *


Flow( 'swellnoise',None, 'math n1=512 output="0.05*cos(x1*6*3.145)" ' )
Flow( 'sig', None,
    '''
    spike n1=512 nsp=5 k1=12,123,214,435 mag=1,-.85,-.71,.5 |
    ricker1
    ''' )

Flow( 'data', ['sig','swellnoise'], 
      'math sig=${SOURCES[1]} output="input+sig" ' )

Result('swellnoise', 'graph' )
Result('sig', 'graph' )
Result('data', 'graph' )

End()

---