#include <liftbase.h>
Inheritance diagram for liftbase::
Public Methods | |
| virtual void | forwardStep (T &vec, const int n) |
| One step in the forward wavelet transform. More... | |
| virtual void | forwardStepRev (T &vec, const int N) |
| Reverse forward transform step. More... | |
| virtual void | forwardTrans (T &vec, const int N) |
| Simple wavelet Lifting Scheme forward transform. More... | |
| virtual void | inverseStep (T &vec, const int n) |
| One inverse wavelet transform step. More... | |
| virtual void | inverseStepRev (T &vec, const int n) |
| Reverse inverse transform step. More... | |
| virtual void | inverseTrans (T &vec, const int N) |
| Default two step Lifting Scheme inverse wavelet transform. More... | |
Protected Types | |
| enum | transDirection { forward = 1, inverse = 2 } |
Protected Methods | |
| void | split (T &vec, int N) |
| Split the vec into even and odd elements, where the even elements are in the first half of the vector and the odd elements are in the second half. More... | |
| void | merge (T &vec, int N) |
| Merge the odd elements from the second half of the N element region in the array with the even elements in the first half of the N element region. More... | |
| virtual void | predict (T &vec, int N, transDirection direction)=0 |
| Predict step, to be defined by the subclass. More... | |
| virtual void | predictRev (T &vec, int N, transDirection direction) |
| Reverse predict step. More... | |
| virtual void | update (T &vec, int N, transDirection direction)=0 |
| Update step, to be defined by the subclass. More... | |
| virtual void | updateRev (T &vec, int N, transDirection direction) |
| Reverse update step. More... | |
Simple lifting scheme wavelets consist of three steps, a split/merge step, predict step and an update step:
The split step divides the elements in an array so that the even elements are in the first half and the odd elements are in the second half.
The merge step is the inverse of the split step. It takes two regions of an array, an odd region and an even region and merges them into a new region where an even element alternates with an odd element.
The predict step calculates the difference between an odd element and its predicted value based on the even elements. The difference between the predicted value and the actual value replaces the odd element.
The predict step operates on the odd elements. The update step operates on the even element, replacing them with a difference between the predict value and the actual odd element. The update step replaces each even element with an average. The result of the update step becomes the input to the next recursive step in the wavelet calculation.
The split and merge methods are shared by all Lifting Scheme wavelet algorithms. This base class provides the transform and inverse transform methods (forwardTrans and inverseTrans). The predict and update methods are abstract and are defined for a particular Lifting Scheme wavelet sub-class.
This is a template version of the lifting scheme base class. The template must be instantiated with an array or an object that acts like an array. Objects that act like arrays define the left hand side and right hand side index operators: []. To allow wavelet transforms based on this base class to be used with the wavelet packet transform, this class makes public both the forward and inverse transforms (forwardTrans and inverseTrans) and the forward and inverse transform steps (forwardStep and inverseStep). These "step" functions are used to calculate the wavelet packet transform.
Instantiating the Template
The liftbase template takes two type arguments:
The simplest example is a wavelet class derived from an instance of the liftbase tempate which takes a double array and has a double element type. This declaration is shown below:
class Haar : public liftbase<double *, double>
An object type can be used for the first template argument, as long as the object supports the '[]' operator, which returns an element whose type is defined by the second argument. In the example below, the packcontainer '[]' operator returns a double.
class Poly : public liftbase<packcontainer, double>
References:
Definition at line 155 of file liftbase.h.
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Definition at line 159 of file liftbase.h. 00159 {
00161 forward = 1,
00163 inverse = 2
00164 } transDirection;
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One step in the forward wavelet transform.
Reimplemented in Daubechies, and haar. Definition at line 262 of file liftbase.h. Referenced by forwardTrans(), Daubechies::forwardTrans(), packtree_base_int::newLevel(), and packtree_base::newLevel().
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Reverse forward transform step. The result of the high pass filter is stored in the lower half of the array and the result of the low pass filter is stored in the upper half. This function should be defined by any subclass that is used for wavelet frequency analysis. Reimplemented in Daubechies, and haar_classicFreq. Definition at line 278 of file liftbase.h. Referenced by packtree_base_int::newLevel(), and packtree_base::newLevel().
00279 {
00280 assert(false);
00281 }
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Simple wavelet Lifting Scheme forward transform. forwardTrans is passed an indexable object. The object must contain a power of two number of data elements. Lifting Scheme wavelet transforms are calculated in-place and the result is returned in the argument array. The result of forwardTrans is a set of wavelet coefficients ordered by increasing frequency and an approximate average of the input data set in vec[0]. The coefficient bands follow this element in powers of two (e.g., 1, 2, 4, 8...). Reimplemented in Daubechies. Definition at line 297 of file liftbase.h. Referenced by testWaveletTrans(), and wave_calc().
00298 {
00299
00300 for (int n = N; n > 1; n = n >> 1) {
00301 forwardStep( vec, n );
00302 }
00303 } // forwardTrans
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One inverse wavelet transform step.
Reimplemented in Daubechies, and haar. Definition at line 309 of file liftbase.h. Referenced by inverseTrans(), Daubechies::inverseTrans(), invpacktree_int::reduce(), and invpacktree::reduce().
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Reverse inverse transform step. Calculate the inverse transform from a high pass filter result stored in the lower half of the array and a low pass filter result stored in the upper half. This function should be defined by any subclass that is used for wavelet frequency analysis. Reimplemented in haar_classicFreq. Definition at line 324 of file liftbase.h. 00325 {
00326 assert( false );
00327 }
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Default two step Lifting Scheme inverse wavelet transform. inverseTrans is passed the result of an ordered wavelet transform, consisting of an average and a set of wavelet coefficients. The inverse transform is calculated in-place and the result is returned in the argument array. Reimplemented in Daubechies. Definition at line 339 of file liftbase.h. Referenced by testWaveletTrans(), and wave_calc().
00340 {
00341
00342 for (int n = 2; n <= N; n = n << 1) {
00343 inverseStep( vec, n );
00344 }
00345 } // inverseTrans
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Merge the odd elements from the second half of the N element region in the array with the even elements in the first half of the N element region. The result will be the combination of the odd and even elements in a region of length N. Definition at line 198 of file liftbase.h. Referenced by ts_trans_int::inverseStep(), inverseStep(), haar::inverseStep(), and haar_classicFreq::inverseStepRev().
00199 {
00200 int half = N >> 1;
00201 int start = half-1;
00202 int end = half;
00203
00204 while (start > 0) {
00205 for (int i = start; i < end; i = i + 2) {
00206 T_elem tmp = vec[i];
00207 vec[i] = vec[i+1];
00208 vec[i+1] = tmp;
00209 }
00210 start = start - 1;
00211 end = end + 1;
00212 }
00213 }
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Predict step, to be defined by the subclass.
Reimplemented in Daubechies, haar, haar_classic, line, and line_int. Referenced by forwardStep(), haar::forwardStep(), inverseStep(), and haar::inverseStep().
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Reverse predict step. The predict step applied the high pass filter to the data set and places the result in the upper half of the array. The reverse predict step applies the high pass filter and places the result in the lower half of the array. This reverse predict step is only used by wavelet packet frequency analysis algorithms. The default version of this algorihtm does nothing. Reimplemented in haar_classicFreq. Definition at line 238 of file liftbase.h. Referenced by haar_classicFreq::forwardStepRev(), and haar_classicFreq::inverseStepRev().
00238 {};
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Split the vec into even and odd elements, where the even elements are in the first half of the vector and the odd elements are in the second half.
Definition at line 173 of file liftbase.h. Referenced by ts_trans_int::forwardStep(), forwardStep(), haar::forwardStep(), and haar_classicFreq::forwardStepRev().
00174 {
00175
00176 int start = 1;
00177 int end = N - 1;
00178
00179 while (start < end) {
00180 for (int i = start; i < end; i = i + 2) {
00181 T_elem tmp = vec[i];
00182 vec[i] = vec[i+1];
00183 vec[i+1] = tmp;
00184 }
00185 start = start + 1;
00186 end = end - 1;
00187 }
00188 }
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Update step, to be defined by the subclass.
Reimplemented in Daubechies, haar, haar_classic, line, and line_int. Referenced by forwardStep(), haar::forwardStep(), inverseStep(), and haar::inverseStep().
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Reverse update step.
Reimplemented in haar_classicFreq. Definition at line 255 of file liftbase.h. Referenced by haar_classicFreq::forwardStepRev(), and haar_classicFreq::inverseStepRev().
00255 {}
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1.2.8.1 written by Dimitri van Heesch,
© 1997-2001