Wavelet-based signal de-noising via simple singularities approximation
Signal Processing
Combined image compression and denoising using wavelets
Image Communication
EURASIP Journal on Applied Signal Processing
A Fast Scheme for Multiscale Signal Denoising
ICIAR '08 Proceedings of the 5th international conference on Image Analysis and Recognition
Image Denoising Using Similarities in the Time-Scale Plane
ACIVS '08 Proceedings of the 10th International Conference on Advanced Concepts for Intelligent Vision Systems
Hierarchical segmentation-based image coding using hybrid quad-binary trees
IEEE Transactions on Image Processing
On bounds of shift variance in two-channel multirate filter banks
IEEE Transactions on Signal Processing
Depth and depth-color coding using shape-adaptive wavelets
Journal of Visual Communication and Image Representation
Analytical footprints: compact representation of elementary singularities in wavelet bases
IEEE Transactions on Signal Processing
Change detection in time series data using wavelet footprints
SSTD'05 Proceedings of the 9th international conference on Advances in Spatial and Temporal Databases
Time-Scale Similarities for Robust Image De-noising
Journal of Mathematical Imaging and Vision
Hi-index | 35.69 |
Wavelet-based algorithms have been successful in different signal processing tasks. The wavelet transform is a powerful tool because it manages to represent both transient and stationary behaviors of a signal with few transform coefficients. Discontinuities often carry relevant signal information, and therefore, they represent a critical part to analyze. We study the dependency across scales of the wavelet coefficients generated by discontinuities. We start by showing that any piecewise smooth signal can be expressed as a sum of a piecewise polynomial signal and a uniformly smooth residual (Theorem 1). We then introduce the notion of footprints, which are scale space vectors that model discontinuities in piecewise polynomial signals exactly. We show that footprints form an overcomplete dictionary and develop efficient and robust algorithms to find the exact representation of a piecewise polynomial function in terms of footprints. This also leads to efficient approximation of piecewise smooth functions. Finally, we focus on applications and show that algorithms based on footprints outperform standard wavelet methods in different applications such as denoising, compression, and (nonblind) deconvolution. In the case of compression, we also prove that at high rates, footprint-based algorithms attain optimal performance (Theorem 3).