filterbank

R2026b

Shearlet system filters

Syntax

psi = filterbank(sls)

[psi,scale] = filterbank(sls)

[psi,scale,shear] = filterbank(sls)

[psi,scale,shear,cone] = filterbank(sls)

Description

psi = filterbank(sls) returns the Fourier transforms of the shearlet filters defined by the shearlet system sls as a 3-D real-valued array. The array size is M-by-N-by-K, where M and N are the values of the two-element row vector ImageSize of sls. K is the number of shearlets including the lowpass filter, K = numshears(sls) + 1.

[psi,scale] = filterbank(sls) returns the scale parameters of the shearlet filters as a K-by-1 integer vector. K is the number of shearlets including the lowpass filter, K = numshears(sls) + 1.

[psi,scale,shear] = filterbank(sls) returns the shearing parameters of the shearlet filters as a K-by-1 integer vector. K is the number of shearlets including the lowpass filter, K = numshears(sls) + 1.

[psi,scale,shear,cone] = filterbank(sls) returns the frequency cones of the shearlet filters as a K-by-1 cell array of characters. K is the number of shearlets including the lowpass filter, K = numshears(sls) + 1.

Examples

Obtain Shearlet Filters

Load an image. Create a shearlet system that can be used with the image.

load clown
sls = shearletSystem('ImageSize',size(X))

sls = 
  shearletSystem with properties:

         ImageSize: [200 320]
         NumScales: 4
    PreserveEnergy: 0
     TransformType: 'real'
    FilterBoundary: 'periodic'
         Precision: 'double'

Obtain the shearlet filters defined by the shearlet system.

psi = filterbank(sls);

Obtain the shearlet transform of the image.

cfs = sheart2(sls,X);

Confirm that the size of the third dimension of psi is equal to the size of the third dimension of cfs.

[size(psi,3) size(cfs,3)]

ans = 1×2

    41    41

Plot Shearlet Filters

Create a complex-valued shearlet system for 256-by-256 images with truncated boundaries and four scales.

sls = shearletSystem('TransformType','complex',...
    'ImageSize',[256 256],...
    'FilterBoundary','truncated',...
    'NumScales',4);

Obtain the shearlet filters and their geometric interpretations.

[psi,scale,shear,cone] = filterbank(sls);

Different scales can have a different number of shears. The scales in the shearlet system range from 0 to 3 inclusive. Find the range of shears per scale.

for k=0:3
    ind = find(scale==k);
    fprintf('scale: %d  shear range: [%d:%d]\n',...
        k,min(shear(ind)),max(shear(ind)))
end

scale: 0  shear range: [-1:1]
scale: 1  shear range: [-2:2]
scale: 2  shear range: [-2:2]
scale: 3  shear range: [-3:3]

Display the unique frequency cone labels.

unique(cone)

ans = 5×1 cell
    {'B'}
    {'L'}
    {'R'}
    {'T'}
    {'X'}

Find the shearlet filter at scale 2 with shear parameter equal to 1 and whose support is in the 'R' frequency cone.

vScale = 2;
vShear = 1;
vCone = 'R';
ind = (scale'==vScale)&(shear'==vShear)&([cone{:}]==vCone);
shFilter = psi(:,:,ind);

Plot the shearlet filter.

omegax = -1/2:1/256:1/2-1/256;
omegay = omegax;
surf(omegax,flip(omegay),shFilter,'EdgeColor','none')
view(0,90)
xlabel('\omega_x')
ylabel('\omega_y')
str = sprintf('Shearlet Filter: Scale %d / Shear %d / Cone %c',...
    vScale,vShear,vCone);
title(str)
axis equal
axis tight

Plot the supports of all scale 2 shearlet filters with shear parameters equal to $$\pm$$2. Areas where filter supports overlap have maximum brightness.

vScale = 2;
vShear = 2;
ind = find((scale==vScale).*(abs(shear)==vShear));
tmp = zeros(size(psi,1),size(psi,2));
for k=1:length(ind)
    tmp = tmp+(psi(:,:,ind(k))~=0);
end
surf(omegax,flip(omegay),double(tmp),'EdgeColor','none')
view(0,90)
xlabel('\omega_x')
ylabel('\omega_y')
str = sprintf('Filter Supports: Scale %d / Abs(Shear) %d',...
    vScale,vShear);
title(str)
axis equal
axis tight
colormap gray
colorbar

Input Arguments

sls — Shearlet system

shearletSystem object

Shearlet system, specified as a shearletSystem object.

Output Arguments

psi — Fourier transforms of shearlet filters

real-valued 3-D array

Fourier transforms of the shearlet filters defined by the shearlet system, returned as a 3-D real-valued array. The array size is M-by-N-by-K, where M and N are the first and second elements, respectively, of the ImageSize value of sls. K is the number of shearlets including the lowpass filter, K = numshears(sls) + 1. The first element in the third dimension of psi corresponds to the lowpass filter. The subsequent elements correspond to the shearlets.

The data type of psi matches the Precision value of the shearlet system.

Data Types: single | double

scale — Scale parameters

integer vector

Scale parameters of the shearlet filters defined by the shearlet system, returned as a K-by-1 integer vector. K is the number of shearlets including the lowpass filter, K = numshears(sls) + 1. The first element of scale, −1, corresponds to the lowpass filter. The remaining elements of scale correspond to the shearlet filters.

The data type of scale matches the Precision value of the shearlet system.

Data Types: single | double

shear — Shearing parameters

integer vector

Shearing parameters of the shearlet filters defined by the shearlet system, returned as a K-by-1 integer vector. K is the number of shearlets including the lowpass filter, K = numshears(sls) + 1. The shear values at scale S range from −ceil(2^(S/2)) to ceil(2^(S/2)) inclusive. The first element of shear, 0, corresponds to the lowpass filter. The remaining elements of shear denote the shears for the corresponding shearlet filters.

The data type of shear matches the Precision value of the shearlet system.

Data Types: single | double

cone — Frequency cones

cell array of characters

Frequency cones of the shearlet filters defined by the shearlet system, returned as a K-by-1 cell array of characters. K is the number of shearlets including the lowpass filter, K = numshears(sls) + 1. The first element of cone, 'X', corresponds to the lowpass filter. The remaining elements of cone are the frequency cones in which the corresponding shearlet filters have their frequency support.

For complex-valued shearlets, the frequency plane is divided into four cones: 'R' (right), 'T' (top), 'L' (left), and 'B' (bottom). For real-valued shearlets, the frequency cones are 'H' (horizontal) and 'V' (vertical).

Extended Capabilities

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

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

The filterbank function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

Version History

Introduced in R2019b

R2026b: Use thread-based environments

You can use filterbank in thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.