Tuesday, October 15, 2019 - 4:15pm - 6:00pm
- Wavelet-Domain Low-Rank/Group-Sparse Destriping for Hyperspectral Imagery
Jim Fowler (Mississippi State University)
Pushbroom acquisition of hyperspectral imagery is prone to striping artifacts in the along-track direction. A hyperspectral destriping algorithm is proposed such that subbands of a 3D wavelet transform most effected by pushbroom stripes---namely, those with spatially vertical orientation---are the exclusive focus of destriping. The proposed method features an iterative image decomposition composed of a low-rank model for the stripes coupled with a group-sparse prior on the wavelet coefficients of the subbands in question. While low-rank stripe models have been widely used in the past, they typically have been deployed in conjunction with a total-variation prior on the image which is prone to over-smoothing and residual stripe artifacts. On the other hand, the proposed group-sparse prior not only captures the well-known sparse nature of wavelet coefficients but also capitalizes on their vertical clustering in the subbands in question. Additionally, while many prior destriping methods are wavelet-based, they employ 2D transforms band by band. In contrast, the proposed 3D wavelet transform provides greater concentration of stripe information into fewer wavelet coefficients, leading to more effective destriping. Experimental results on both synthetically striped imagery as well as real striped imagery from an actual hyperspectral sensor demonstrate superior image quality for the proposed method as compared to other state-of-the-art methods.
- On Non-Convex Regularization for Convex Signal Processing
Ivan Selesnick (New York University)
Some effective and systematic approaches for nonlinear signal processing are based on sparse and low-rank signal models. Often, the L1 norm (or nuclear norm) is used, but this tends to underestimate the true values. We present non-convex alternatives to the L1 norm (and nuclear norm). Unlike other non-convex regularizers, the proposed regularizer is designed to maintain the convexity of the objective function to be minimized. Thus, we can retain beneficial properties of both convex and non-convex regularization. The new regularizer can be understood in terms of a generalized Moreau envelope. We present new results applying these ideas to total variation signal denoising.
- The iterative convolution-thresholding method (ICTM) for image segmentation
Dong Wang (The University of Utah)
We propose a novel iterative convolution-thresholding method (ICTM) that is applicable to a range of variational models for image segmentation. A variational model usually minimizes an energy functional consisting of a fidelity term and a regularization term. In the ICTM, the interface between two different segment domains is implicitly represented by their characteristic functions. The fidelity term is then written as a linear functional of the characteristic functions and the regularized term is approximated by a functional of characteristic functions in terms of heat kernel convolution. This allows us to design an iterative convolution-thresholding method to minimize the approximate energy. The method is simple, efficient and enjoys the energy-decaying property. Numerical experiments show that the method is easy to implement, robust and applicable to various image segmentation models.