ihaart2

Inverse 2-D Haar wavelet transform

Syntax

xrec = ihaart2(a,h,v,d)

xrec = ihaart2(a,h,v,d,level)

xrec = ihaart2(___,integerflag)

Description

xrec = ihaart2(a,h,v,d) returns the inverse 2-D Haar transform, xrec, for the approximation coefficients, a, and the horizontal, vertical, and diagonal detail coefficients, h, v, and d. All the inputs, a, h, v, and d, are outputs of haart2.

xrec = ihaart2(a,h,v,d,level) returns the inverse 2-D Haar transform at the specified level.

xrec = ihaart2(___,integerflag) specifies how the inverse 2-D Haar transform handles integer-valued data, using any of the previous syntaxes.

Examples

Inverse 2-D Haar Transform of an Image

Obtain the inverse 2-D Haar transform of image and view the reconstructed image.

Load the image and obtain its 2-D Haar transform.

im = imread('mandrill.png');
[a,h,v,d] = haart2(im);

Use the inverse 2-D Haar transform to reconstruct the image.

xrec = ihaart2(a,h,v,d);

Compare the original and reconstructed images.

imagesc(im)
title('Original RGB Image')

figure
imagesc(uint8(xrec))
title('Reconstructed RGB Image')

Inverse 2-D Haar Transform of Image Limited to Specified Level

Obtain the 2-D Haar transform of an image limiting the transform to 2 levels.

Load and view the image of a cameraman.

im = imread('cameraman.tif');
imagesc(im)

Obtain the 2-D Haar transform using the default maximum number of levels.

[a,h,v,d] = haart2(im);

Reconstruct the image using the inverse 2-D Haar transform and view the image. Notice the near-perfect reconstruction.

xrec = ihaart2(a,h,v,d);
imagesc(xrec)

Reconstruct and view the image using the inverse 2-D Haar transform, limited to level 2. Level 2 corresponds to the fourth scale because scale is defined as $$2^j$$, where j is the level.

xrec1 = ihaart2(a,h,v,d,2);
imagesc(xrec1)

Using fewer levels returns the average of the original image at level 2.

Inverse 2-D Haar Transform of Image Limited to Integer Data

Obtain the 2-D Haar transform of an image limiting the transform to integer data.

Load the image of a cameraman.

im = imread('cameraman.tif');

Obtain the 2-D Haar transform using the 'integer' flag.

[a,h,v,d]=haart2(im,'integer');

Reconstruct the image using the inverse 2-D Haar transform and view the image.

xrec = ihaart2(a,h,v,d,'integer');
imagesc(xrec)

Use integer data when you need to reduce the amount of memory used compared to noninteger data.

Input Arguments

a — Approximation coefficients

scalar | matrix

Approximation coefficients, specified as a scalar or matrix of coefficients, depending on the level to which the 2-D Haar transform was calculated. a is an output from the haart2 function. Approximation, or scaling, coefficients are a lowpass representation of the input. If a and the elements of h, v, and d, are vectors, xrec is a vector. If a and the elements of h, v, and d are matrices, xrec is a matrix, where each column is the inverse 2-D Haar transform of the corresponding columns in a and h, v, or d.

Data Types: single | double

h — Horizontal detail coefficients

matrix | cell array

Horizontal detail coefficients by level, specified as a matrix or cell array of matrices. h is an output from the haart2 function. If h is a matrix, the 2-D Haar transform was computed only down to one level coarser in resolution.

Data Types: single | double

v — Vertical detail coefficients

matrix or | cell array

Vertical detail coefficients by level, specified as a matrix or cell array of matrices. v is an output from the haart2 function. If v is a matrix, the 2-D Haar transform was computed only down to one level coarser in resolution.

Data Types: single | double

d — Diagonal detail coefficients

matrix or | cell array

Diagonal detail coefficients by level, specified as a matrix or cell array of matrices. d is an output from the haart2 function. If d is a matrix, the 2-D Haar transform was computed only down to one level coarser in resolution.

Data Types: single | double

level — Maximum level

0 (default) | nonnegative integer

Maximum level to which to invert the Haar transform, specified as a nonnegative integer. If h is a cell array, level is less than or equal to length(h)-1. If h is a vector or matrix, level must equal 0 or be unspecified.

integerflag — Integer-valued data handling

'noninteger' (default) | 'integer'

Integer-valued data handling, specified as either 'noninteger' or 'integer'. 'noninteger' does not preserve integer-valued data in the 2-D Haar transform, and 'integer' preserves it. The 'integer' option applies only if all elements of inputs, a, h, v, and d, are integer-valued. The inverse 2-D Haar transform algorithm, however, uses floating-point arithmetic.

Output Arguments

xrec — Inverse 2-D Haar wavelet transform

matrix

2-D Haar wavelet transform, returned as a matrix.

Data Types: single | double

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.