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Fast computation of the discrete Walsh and Hadamard transforms
1Centre for Signal Processing and Communications, Department of Electrical and Computer Engineering, Concordia University, Montreal, P.Q., Canada H3G 1M8.
Summary
This study introduces new algorithms for discrete Walsh transform (DWT) and discrete Hadamard transform (DHAT) in image processing. These novel methods enhance computational efficiency and reduce processing operations for image coding and pattern recognition.
Area of Science:
- Digital Signal Processing
- Image Processing
Background:
- Discrete Walsh Transform (DWT) and Discrete Hadamard Transform (DHAT) are crucial for image processing tasks.
- Existing algorithms can be computationally intensive and require complex operations.
Purpose of the Study:
- To develop novel, more efficient algorithms for DWT and DHAT.
- To reduce computational complexity and operational overhead in image processing.
Main Methods:
- A new DWT algorithm is derived by decomposing a modified DWT relation into smaller-sized transforms using vectorized quantities.
- A new sequency-ordered DHAT algorithm is also presented.
Main Results:
- The proposed algorithms exhibit more regular structures.
- Significant reduction in data swapping, array-index updating, and bit-reversal operations.
- Analysis of computational complexity and execution time performance demonstrates improvements over existing methods.
Conclusions:
- The new DWT and DHAT algorithms offer enhanced efficiency for image processing applications.
- The streamlined approach simplifies implementation and improves performance.
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