Image Analysis Using a Dual-Tree M-Band Wavelet Transform
We propose a 2D generalization to the M-band case of the dual-tree decomposition structure (initially proposed by N. Kingsbury and further investigated by I. Selesnick) based on a Hilbert pair of wavelets. We particularly address (i) the construction of the dual basis and (ii) the resulting directional analysis. We also revisit the necessary pre-processing stage in the M-band case. While several reconstructions are possible because of the redundancy of the representation, we propose a new optimal signal reconstruction technique, which minimizes potential estimation errors. The effectiveness of the proposed M- band decomposition is demonstrated via denoising comparisons on several image types (natural, texture, seismics), with various M-band wavelets and thresholding strategies. Signicant improvements in terms of both overall noise reduction and direction preservation are observed.
Summary
This paper extends the dual-tree wavelet decomposition to the 2D M-band case, detailing the construction of a Hilbert-pair dual basis and the resulting directional analysis. It also presents preprocessing requirements for M-band systems and proposes an optimal reconstruction method, with empirical denoising comparisons across natural, texture, and seismic images.
Key Takeaways
- Describe how to construct an M-band dual-tree wavelet basis from Hilbert-pair wavelets for 2D signals.
- Evaluate the directional analysis advantages introduced by the M-band dual-tree structure compared with standard dyadic transforms.
- Implement the necessary pre-processing and M-band filter-bank design considerations for stable decomposition and reconstruction.
- Apply the proposed optimal reconstruction technique to minimize estimation errors in redundant M-band representations.
- Compare denoising performance across image types using different M-band wavelets and thresholding strategies to select effective configurations.
Who Should Read This
Signal and image processing engineers or researchers with interest in multiscale directional transforms who want to implement or evaluate M-band dual-tree wavelets for image analysis and denoising.
Still RelevantAdvanced
Related Documents
- A New Approach to Linear Filtering and Prediction Problems TimelessAdvanced
- An Introduction To Compressive Sampling TimelessIntermediate
- Lecture Notes on Elliptic Filter Design TimelessAdvanced
- Digital Envelope Detection: The Good, the Bad, and the Ugly TimelessIntermediate
- The World's Most Interesting FIR Filter Equation: Why FIR Filters Can Be Line... TimelessAdvanced
