Multiscale Hierarchical Decomposition of Images with Applications to Deblurring, Denoising and Segmentation
Abstract
We extend the ideas introduced in [TNV04] for hierarchical multiscale decompositions of images. Viewed as a function f 2 L2"", a given image is hierarchically decomposed into the sum or product of simpler "atoms" u(sub k), where uk extracts a more refined information from the previous scale u(sub k-1). To this end, the u(sub k)'s are obtained as dyadically scaled minimizers of standard functionals arising in image analysis. Thus, starting with v(sub -1):= f and letting v(sub k) denote the residual at a given dyadic scale, lambda(sub k) approximately equal to 2(exp k), then the recursive step [u(sub k), v(sub k)] = arginfQ(sub T) (v(sub k-1), lambda(sub k)leads to the desired hierarchical decomposition, f approximately equal to SUM(Tu(sub )k; here T is a blurring operator. We characterize such Q(subT) -minimizers (by duality) and expand our previous energy estimates of the data f in terms of ||u(sub k)||. Numerical results illustrate applications of the new hierarchical multiscale decomposition for blurry images, images with additive and multiplicative noise and image segmentation.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 04, 2007
- Accession Number
- ADA474869
Entities
People
- Eitan Tadmor
- Luminita Vese
- Suzanne Nezzar
Organizations
- University of Maryland