Inverse shearlet transform
Perfect Reconstruction of Shearlet Transform
Load an image and create a shearlet system that can be applied to the image.
load shapes [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
cfs — Shearlet transform coefficients
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.
isheart2 function assumes
sls is the
same shearlet system used to obtain the transform coefficients
Complex Number Support: Yes