# upwlev2

Single-level reconstruction of 2-D wavelet decomposition

## Description

## Examples

### Perform Single-Level Reconstruction of 2-D Wavelet Decomposition

Load an image.

```
load porche
image(X)
colormap(map)
```

Save the current extension mode, and set the extension mode to zero-padding.

origmode = dwtmode("status","nodisp"); dwtmode("zpd","nodisp")

Obtain the DWT decomposition of the image down to level 2. Use the Haar wavelet.

```
wv = "haar";
[c,s] = wavedec2(X,2,wv);
size(c)
```

`ans = `*1×2*
1 262144

s

`s = `*4×2*
128 128
128 128
256 256
512 512

Use the `appcoef2`

function to extract the approximation coefficients from the wavelet decomposition structure [`c`

,`s`

].

a = appcoef2(c,s,wv); size(a)

`ans = `*1×2*
128 128

Perform the single-level reconstruction of the wavelet decomposition structure [`c`

,`s`

]. Also obtain the approximation matrix at level 2. Confirm the total number of coefficients has not changed, and the approximation coefficients obtained using `appcoef2`

and `upwlev2`

are equal.

[nc,ns,ca] = upwlev2(c,s,wv); size(nc)

`ans = `*1×2*
1 262144

ns

`ns = `*3×2*
256 256
256 256
512 512

max(max(abs(a-ca)))

ans = 0

Restore the original extension mode.

`dwtmode(origmode,"nodisp")`

## Input Arguments

`wname`

— Analyzing wavelet

character vector | string scalar

Analyzing wavelet, specified as a character vector or string scalar.
`wname`

must specify the same wavelet used to obtain
the original wavelet decomposition structure
`[`

.
The `c`

,`s`

]`wavedec2`

function supports
only orthogonal and biorthogonal wavelets. See `wfilters`

for a list of
orthogonal and biorthogonal wavelets.

**Data Types: **`char`

| `string`

`LoR,HiR`

— Wavelet reconstruction filters

vectors

Wavelet reconstruction filters, specified as a pair of even-length
real-valued vectors. `LoR`

is the lowpass reconstruction
filter, and `HiR`

is the highpass reconstruction filter.
`LoR`

and `HiR`

must correspond to the
wavelet used to obtain the original wavelet decomposition structure
`[`

.
The lengths of `c`

,`s`

]`LoR`

and `HiR`

must be
equal. See `wfilters`

for a list of
orthogonal and biorthogonal wavelets.

**Data Types: **`double`

## Output Arguments

`nc`

— Wavelet decomposition

vector

Wavelet decomposition, returned as a vector. The vector contains the
wavelet coefficients. `[c,s]`

is a decomposition at level

, so
*n* = size(s,1)-2`[nc,ns]`

is the same decomposition at level
*n*-1. The bookkeeping matrix `ns`

contains the contains the dimensions of the wavelet coefficients by level
and is used to parse the wavelet decomposition vector
`nc`

.

**Data Types: **`double`

`ns`

— Bookkeeping matrix

vector

Bookkeeping matrix, returned as a matrix of positive integers. The
bookkeeping matrix is used to parse the coefficients in the wavelet
decomposition `nc`

by level.

**Data Types: **`double`

`ca`

— Approximation matrix

vector

Approximation matrix at level *n*, where

.*n* =
size(`s`

,1)-2

If `c`

and `s`

are obtained from an
indexed image analysis or a truecolor image analysis,
`ca`

is an
*m*-by-*n* matrix or an
*m*-by-*n*-by-3 array, respectively.
For more information, see `wavedec2`

.

For more information on image formats, see `image`

and `imfinfo`

.

**Data Types: **`double`

## Version History

**Introduced before R2006a**

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