<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="X-UA-Compatible" content="IE=Edge" />
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>Inverse Stationary Wavelet Transform — PyWavelets Documentation</title>
<link rel="stylesheet" href="../_static/nature.css" type="text/css" />
<link rel="stylesheet" href="../_static/pygments.css" type="text/css" />
<script type="text/javascript" id="documentation_options" data-url_root="../" src="../_static/documentation_options.js"></script>
<script type="text/javascript" src="../_static/jquery.js"></script>
<script type="text/javascript" src="../_static/underscore.js"></script>
<script type="text/javascript" src="../_static/doctools.js"></script>
<script type="text/javascript" src="../_static/language_data.js"></script>
<script async="async" type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
<link rel="search" type="application/opensearchdescription+xml"
title="Search within PyWavelets Documentation"
href="../_static/opensearch.xml"/>
<link rel="shortcut icon" href="../_static/favicon.ico"/>
<link rel="index" title="Index" href="../genindex.html" />
<link rel="search" title="Search" href="../search.html" />
<link rel="next" title="Wavelet Packets" href="wavelet-packets.html" />
<link rel="prev" title="Stationary Wavelet Transform" href="swt-stationary-wavelet-transform.html" />
<meta name="description" content="PyWavelets is a scientific Python module for Wavelet Transform calculations."/>
<meta name="keywords" content="PyWavelets, wavelets, Python, wavelet transform, discrete wavelet transform, dwt, idwt, swt, wavelet packets, stationary wavelet transform, pywt"/>
<meta name="author" content="Filip Wasilewski"/>
<meta name="Distribution" content="Global"/>
<meta name="Robots" content="INDEX,FOLLOW"/>
<script type="text/javascript">
(function ($) {
$(document).ready(function () {
$("#toggle-edit-info").click(function (e) {
e.preventDefault();
$("#edit-info").toggle();
});
});
})(jQuery);
</script>
<script type="text/javascript">
var _gaq = _gaq || [];
_gaq.push(['_setAccount', 'UA-3396395-3']);
_gaq.push(['_trackPageview']);
(function () {
var ga = document.createElement('script');
ga.type = 'text/javascript';
ga.async = true;
ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js';
var s = document.getElementsByTagName('script')[0];
s.parentNode.insertBefore(ga, s);
})();
</script>
</head><body>
<div class="related" role="navigation" aria-label="related navigation">
<h3>Navigation</h3>
<ul>
<li class="right" style="margin-right: 10px">
<a href="../genindex.html" title="General Index"
accesskey="I">index</a></li>
<li class="right" >
<a href="wavelet-packets.html" title="Wavelet Packets"
accesskey="N">next</a> |</li>
<li class="right" >
<a href="swt-stationary-wavelet-transform.html" title="Stationary Wavelet Transform"
accesskey="P">previous</a> |</li>
<li><a href="../index.html">Home »</a></li>
<li class="nav-item nav-item-1"><a href="index.html" accesskey="U">API Reference</a> »</li>
</ul>
</div>
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<div class="section" id="inverse-stationary-wavelet-transform">
<span id="ref-iswt"></span><h1>Inverse Stationary Wavelet Transform<a class="headerlink" href="#inverse-stationary-wavelet-transform" title="Permalink to this headline">¶</a></h1>
<p>Inverse <a class="reference internal" href="swt-stationary-wavelet-transform.html#ref-swt"><span class="std std-ref">stationary wavelet transforms</span></a> are provided.</p>
<p><strong>Note</strong>: These inverse transforms are not yet optimized for speed. Only, the
n-dimensional inverse transform currently has <code class="docutils literal notranslate"><span class="pre">axes</span></code> support.</p>
<div class="section" id="multilevel-1d-iswt">
<h2>Multilevel 1D <code class="docutils literal notranslate"><span class="pre">iswt</span></code><a class="headerlink" href="#multilevel-1d-iswt" title="Permalink to this headline">¶</a></h2>
<dl class="function">
<dt id="pywt.iswt">
<code class="descclassname">pywt.</code><code class="descname">iswt</code><span class="sig-paren">(</span><em>coeffs</em>, <em>wavelet</em><span class="sig-paren">)</span><a class="headerlink" href="#pywt.iswt" title="Permalink to this definition">¶</a></dt>
<dd><p>Multilevel 1D inverse discrete stationary wavelet transform.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first docutils">
<dt><strong>coeffs</strong> <span class="classifier-delimiter">:</span> <span class="classifier">array_like</span></dt>
<dd><p class="first">Coefficients list of tuples:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[(</span><span class="n">cAn</span><span class="p">,</span> <span class="n">cDn</span><span class="p">),</span> <span class="o">...</span><span class="p">,</span> <span class="p">(</span><span class="n">cA2</span><span class="p">,</span> <span class="n">cD2</span><span class="p">),</span> <span class="p">(</span><span class="n">cA1</span><span class="p">,</span> <span class="n">cD1</span><span class="p">)]</span>
</pre></div>
</div>
<p class="last">where cA is approximation, cD is details. Index 1 corresponds to
<code class="docutils literal notranslate"><span class="pre">start_level</span></code> from <code class="docutils literal notranslate"><span class="pre">pywt.swt</span></code>.</p>
</dd>
<dt><strong>wavelet</strong> <span class="classifier-delimiter">:</span> <span class="classifier">Wavelet object or name string</span></dt>
<dd><p class="first last">Wavelet to use</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>1D array of reconstructed data.</strong></dt>
<dd></dd>
</dl>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Examples</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">pywt</span>
<span class="gp">>>> </span><span class="n">coeffs</span> <span class="o">=</span> <span class="n">pywt</span><span class="o">.</span><span class="n">swt</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">6</span><span class="p">,</span><span class="mi">7</span><span class="p">,</span><span class="mi">8</span><span class="p">],</span> <span class="s1">'db2'</span><span class="p">,</span> <span class="n">level</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">pywt</span><span class="o">.</span><span class="n">iswt</span><span class="p">(</span><span class="n">coeffs</span><span class="p">,</span> <span class="s1">'db2'</span><span class="p">)</span>
<span class="go">array([ 1., 2., 3., 4., 5., 6., 7., 8.])</span>
</pre></div>
</div>
</dd></dl>
</div>
<div class="section" id="multilevel-2d-iswt2">
<h2>Multilevel 2D <code class="docutils literal notranslate"><span class="pre">iswt2</span></code><a class="headerlink" href="#multilevel-2d-iswt2" title="Permalink to this headline">¶</a></h2>
<dl class="function">
<dt id="pywt.iswt2">
<code class="descclassname">pywt.</code><code class="descname">iswt2</code><span class="sig-paren">(</span><em>coeffs</em>, <em>wavelet</em><span class="sig-paren">)</span><a class="headerlink" href="#pywt.iswt2" title="Permalink to this definition">¶</a></dt>
<dd><p>Multilevel 2D inverse discrete stationary wavelet transform.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first docutils">
<dt><strong>coeffs</strong> <span class="classifier-delimiter">:</span> <span class="classifier">list</span></dt>
<dd><p class="first">Approximation and details coefficients:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span>
<span class="p">(</span><span class="n">cA_n</span><span class="p">,</span>
<span class="p">(</span><span class="n">cH_n</span><span class="p">,</span> <span class="n">cV_n</span><span class="p">,</span> <span class="n">cD_n</span><span class="p">)</span>
<span class="p">),</span>
<span class="o">...</span><span class="p">,</span>
<span class="p">(</span><span class="n">cA_2</span><span class="p">,</span>
<span class="p">(</span><span class="n">cH_2</span><span class="p">,</span> <span class="n">cV_2</span><span class="p">,</span> <span class="n">cD_2</span><span class="p">)</span>
<span class="p">),</span>
<span class="p">(</span><span class="n">cA_1</span><span class="p">,</span>
<span class="p">(</span><span class="n">cH_1</span><span class="p">,</span> <span class="n">cV_1</span><span class="p">,</span> <span class="n">cD_1</span><span class="p">)</span>
<span class="p">)</span>
<span class="p">]</span>
</pre></div>
</div>
<p class="last">where cA is approximation, cH is horizontal details, cV is
vertical details, cD is diagonal details and n is the number of
levels. Index 1 corresponds to <code class="docutils literal notranslate"><span class="pre">start_level</span></code> from <code class="docutils literal notranslate"><span class="pre">pywt.swt2</span></code>.</p>
</dd>
<dt><strong>wavelet</strong> <span class="classifier-delimiter">:</span> <span class="classifier">Wavelet object or name string, or 2-tuple of wavelets</span></dt>
<dd><p class="first last">Wavelet to use. This can also be a 2-tuple of wavelets to apply per
axis.</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>2D array of reconstructed data.</strong></dt>
<dd></dd>
</dl>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Examples</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">pywt</span>
<span class="gp">>>> </span><span class="n">coeffs</span> <span class="o">=</span> <span class="n">pywt</span><span class="o">.</span><span class="n">swt2</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">],[</span><span class="mi">5</span><span class="p">,</span><span class="mi">6</span><span class="p">,</span><span class="mi">7</span><span class="p">,</span><span class="mi">8</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="mi">9</span><span class="p">,</span><span class="mi">10</span><span class="p">,</span><span class="mi">11</span><span class="p">,</span><span class="mi">12</span><span class="p">],[</span><span class="mi">13</span><span class="p">,</span><span class="mi">14</span><span class="p">,</span><span class="mi">15</span><span class="p">,</span><span class="mi">16</span><span class="p">]],</span>
<span class="gp">... </span> <span class="s1">'db1'</span><span class="p">,</span> <span class="n">level</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">pywt</span><span class="o">.</span><span class="n">iswt2</span><span class="p">(</span><span class="n">coeffs</span><span class="p">,</span> <span class="s1">'db1'</span><span class="p">)</span>
<span class="go">array([[ 1., 2., 3., 4.],</span>
<span class="go"> [ 5., 6., 7., 8.],</span>
<span class="go"> [ 9., 10., 11., 12.],</span>
<span class="go"> [ 13., 14., 15., 16.]])</span>
</pre></div>
</div>
</dd></dl>
</div>
<div class="section" id="multilevel-n-dimensional-iswtn">
<h2>Multilevel n-dimensional <code class="docutils literal notranslate"><span class="pre">iswtn</span></code><a class="headerlink" href="#multilevel-n-dimensional-iswtn" title="Permalink to this headline">¶</a></h2>
<dl class="function">
<dt id="pywt.iswtn">
<code class="descclassname">pywt.</code><code class="descname">iswtn</code><span class="sig-paren">(</span><em>coeffs</em>, <em>wavelet</em>, <em>axes=None</em><span class="sig-paren">)</span><a class="headerlink" href="#pywt.iswtn" title="Permalink to this definition">¶</a></dt>
<dd><p>Multilevel nD inverse discrete stationary wavelet transform.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first docutils">
<dt><strong>coeffs</strong> <span class="classifier-delimiter">:</span> <span class="classifier">list</span></dt>
<dd><p class="first last">[{coeffs_level_n}, …, {coeffs_level_1}]: list of dict</p>
</dd>
<dt><strong>wavelet</strong> <span class="classifier-delimiter">:</span> <span class="classifier">Wavelet object or name string, or tuple of wavelets</span></dt>
<dd><p class="first last">Wavelet to use. This can also be a tuple of wavelets to apply per
axis in <code class="docutils literal notranslate"><span class="pre">axes</span></code>.</p>
</dd>
<dt><strong>axes</strong> <span class="classifier-delimiter">:</span> <span class="classifier">sequence of ints, optional</span></dt>
<dd><p class="first last">Axes over which to compute the inverse SWT. Axes may not be repeated.
The default is <code class="docutils literal notranslate"><span class="pre">None</span></code>, which means transform all axes
(<code class="docutils literal notranslate"><span class="pre">axes</span> <span class="pre">=</span> <span class="pre">range(data.ndim)</span></code>).</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>nD array of reconstructed data.</strong></dt>
<dd></dd>
</dl>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Examples</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">pywt</span>
<span class="gp">>>> </span><span class="n">coeffs</span> <span class="o">=</span> <span class="n">pywt</span><span class="o">.</span><span class="n">swtn</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">],[</span><span class="mi">5</span><span class="p">,</span><span class="mi">6</span><span class="p">,</span><span class="mi">7</span><span class="p">,</span><span class="mi">8</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="mi">9</span><span class="p">,</span><span class="mi">10</span><span class="p">,</span><span class="mi">11</span><span class="p">,</span><span class="mi">12</span><span class="p">],[</span><span class="mi">13</span><span class="p">,</span><span class="mi">14</span><span class="p">,</span><span class="mi">15</span><span class="p">,</span><span class="mi">16</span><span class="p">]],</span>
<span class="gp">... </span> <span class="s1">'db1'</span><span class="p">,</span> <span class="n">level</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">pywt</span><span class="o">.</span><span class="n">iswtn</span><span class="p">(</span><span class="n">coeffs</span><span class="p">,</span> <span class="s1">'db1'</span><span class="p">)</span>
<span class="go">array([[ 1., 2., 3., 4.],</span>
<span class="go"> [ 5., 6., 7., 8.],</span>
<span class="go"> [ 9., 10., 11., 12.],</span>
<span class="go"> [ 13., 14., 15., 16.]])</span>
</pre></div>
</div>
</dd></dl>
</div>
</div>
</div>
</div>
</div>
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
<div class="sphinxsidebarwrapper">
<h3><a href="../index.html">Table of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">Inverse Stationary Wavelet Transform</a><ul>
<li><a class="reference internal" href="#multilevel-1d-iswt">Multilevel 1D <code class="docutils literal notranslate"><span class="pre">iswt</span></code></a></li>
<li><a class="reference internal" href="#multilevel-2d-iswt2">Multilevel 2D <code class="docutils literal notranslate"><span class="pre">iswt2</span></code></a></li>
<li><a class="reference internal" href="#multilevel-n-dimensional-iswtn">Multilevel n-dimensional <code class="docutils literal notranslate"><span class="pre">iswtn</span></code></a></li>
</ul>
</li>
</ul>
<h4>Previous topic</h4>
<p class="topless"><a href="swt-stationary-wavelet-transform.html"
title="previous chapter">Stationary Wavelet Transform</a></p>
<h4>Next topic</h4>
<p class="topless"><a href="wavelet-packets.html"
title="next chapter">Wavelet Packets</a></p><div>
<h3>Quick links</h3>
<ul>
<li><a href="https://github.com/PyWavelets/pywt"><img src="../_static/github.png" height="16" width="16" alt="" /> Fork on Github</a></li>
<li><a href="http://groups.google.com/group/pywavelets"><img src="../_static/comments.png" height="16" width="16" alt="" /> Discussion Group</a></li>
<li><a href="http://wavelets.pybytes.com/"><img src="../_static/wave.png" height="16" width="16" alt="" /> Explore Wavelets</a></li>
</ul>
</div>
<div id="searchbox" style="display: none" role="search">
<h3>Quick search</h3>
<div class="searchformwrapper">
<form class="search" action="../search.html" method="get">
<input type="text" name="q" />
<input type="submit" value="Go" />
<input type="hidden" name="check_keywords" value="yes" />
<input type="hidden" name="area" value="default" />
</form>
</div>
</div>
<script type="text/javascript">$('#searchbox').show(0);</script>
<div id="edit-instructions">
<h3>Edit this document</h3>
<p>
<a href="#" id="toggle-edit-info">
<img src="../_static/page_edit.png" height="16" width="16" alt="" />
The source code of this file is hosted on GitHub. Everyone can
update and fix errors in this document with few clicks -
no downloads needed.
</a>
</p>
<ol id="edit-info" style="display: none;">
<li>
Go to
<i><a href="https://github.com/PyWavelets/pywt/blob/master/doc/source/ref/iswt-inverse-stationary-wavelet-transform.rst" target="_blank">
Inverse Stationary Wavelet Transform
</a></i> on GitHub.
</li>
<li>
Press <b>Edit this file</b> button.
</li>
<li>
Edit file contents using GitHub's text editor in your web browser
</li>
<li>
Fill in the <b>Commit message</b> text box at the end of the page
telling <i>why</i> you did the changes.
Press <b>Propose file change</b> button next to it when done.
</li>
<li>
On <i>Send a pull request</i> page you don't need to fill in text
anymore. Just press <b>Send pull request</b> button.
</li>
<li>
Your changes are now queued for review under project's
<a href="https://github.com/PyWavelets/pywt/pulls" target="_blank">Pull requests</a> tab
on Github.
</li>
</ol>
</div>
</div>
</div>
<div class="clearer"></div>
</div>
<div class="related" role="navigation" aria-label="related navigation">
<h3>Navigation</h3>
<ul>
<li class="right" style="margin-right: 10px">
<a href="../genindex.html" title="General Index"
>index</a></li>
<li class="right" >
<a href="wavelet-packets.html" title="Wavelet Packets"
>next</a> |</li>
<li class="right" >
<a href="swt-stationary-wavelet-transform.html" title="Stationary Wavelet Transform"
>previous</a> |</li>
<li><a href="../index.html">Home »</a></li>
<li class="nav-item nav-item-1"><a href="index.html" >API Reference</a> »</li>
</ul>
</div>
<div class="footer" role="contentinfo">
© Copyright 2006-2019, The PyWavelets Developers.
Last updated on Jan 12, 2019.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.8.3.
</div>
</body>
</html>
