# isheart2

Inverse shearlet transform

## Description

example

imrec = isheart2(sls,cfs) returns the inverse shearlet transform or shearlet synthesis based on the shearlet system sls and the shearlet transform coefficients cfs. The isheart2 function assumes sls is the same shearlet system used to obtain the transform coefficients cfs.

## Examples

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Load an image and create a shearlet system that can be applied to the image.

[numRows,numCols] = size(shapes);
sls = shearletSystem('ImageSize',[numRows numCols],'NumScales',4)
sls =
shearletSystem with properties:

ImageSize: [512 512]
NumScales: 4
PreserveEnergy: 0
TransformType: 'real'
FilterBoundary: 'periodic'
Precision: 'double'

Obtain the shearlet coefficients of the image.

cfs = sheart2(sls,shapes);

Take the inverse transform of the coefficients. Check for perfect reconstruction.

imrec = isheart2(sls,cfs);
norm(imrec-shapes,'fro')
ans = 7.6938e-14

## Input Arguments

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Shearlet system, specified as a shearletSystem object.

Shearlet transform coefficients, specified as a real- or complex-valued 3-D array. The 3-D array cfs is an M-by-N-by-K matrix where M and N are equal to the row and column dimensions of the original image. The size of the third dimension, K, is equal to the number of shearlets including the lowpass filter, K = numshears(sls) + 1.

The isheart2 function assumes sls is the same shearlet system used to obtain the transform coefficients cfs.

Data Types: single | double
Complex Number Support: Yes

## Output Arguments

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Inverse shearlet transform or shearlet synthesis, based on the shearlet system sls and the shearlet transform coefficients cfs. The size of imrec is equal to the size of the original image. The data type of imrec matches the Precision value of the shearlet system.

Data Types: single | double

## Version History

Introduced in R2019b