Article

# Splines in Higher Order TV Regularization.

International Journal of Computer Vision (Impact Factor: 3.62). 01/2006; 70:241-255. DOI: 10.1007/s11263-006-8066-7

Source: DBLP

- [Show abstract] [Hide abstract]

**ABSTRACT:**Removing noise from piecewise constant (PWC) signals is a challenging signal processing problem arising in many practical contexts. For example, in exploration geosciences, noisy drill hole records need to be separated into stratigraphic zones, and in biophysics, jumps between molecular dwell states have to be extracted from noisy fluorescence microscopy signals. Many PWC denoising methods exist, including total variation regularization, mean shift clustering, stepwise jump placement, running medians, convex clustering shrinkage and bilateral filtering; conventional linear signal processing methods are fundamentally unsuited. This paper (part I, the first of two) shows that most of these methods are associated with a special case of a generalized functional, minimized to achieve PWC denoising. The minimizer can be obtained by diverse solver algorithms, including stepwise jump placement, convex programming, finite differences, iterated running medians, least angle regression, regularization path following and coordinate descent. In the second paper, part II, we introduce novel PWC denoising methods, and comparisons between these methods performed on synthetic and real signals, showing that the new understanding of the problem gained in part I leads to new methods that have a useful role to play.Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences 11/2011; 467(2135):3088-3114. · 2.38 Impact Factor -
##### Conference Paper: Two Step Variational Method for Subpixel Optical Flow Computation.

[Show abstract] [Hide abstract]

**ABSTRACT:**We develop an algorithm for the super-resolution optical flow computation by combining variational super-resolution and the variational optical flow computation. Our method first computes the gradient and the spatial difference of a high resolution images from these of low resolution images directly, without computing any high resolution images. Second the algorithm computes optical flow of high resolution image using the results of the first step.Advances in Visual Computing, 5th International Symposium, ISVC 2009, Las Vegas, NV, USA, November 30 - December 2, 2009, Proceedings, Part II; 01/2009 -
##### Article: Generalized methods and solvers for noise removal from piecewise constant signals. II. New methods.

[Show abstract] [Hide abstract]

**ABSTRACT:**Removing noise from signals which are piecewise constant (PWC) is a challenging signal processing problem that arises in many practical scientific and engineering contexts. In the first paper (part I) of this series of two, we presented background theory building on results from the image processing community to show that the majority of these algorithms, and more proposed in the wider literature, are each associated with a special case of a generalized functional, that, when minimized, solves the PWC denoising problem. It shows how the minimizer can be obtained by a range of computational solver algorithms. In this second paper (part II), using this understanding developed in part I, we introduce several novel PWC denoising methods, which, for example, combine the global behaviour of mean shift clustering with the local smoothing of total variation diffusion, and show example solver algorithms for these new methods. Comparisons between these methods are performed on synthetic and real signals, revealing that our new methods have a useful role to play. Finally, overlaps between the generalized methods of these two papers and others such as wavelet shrinkage, hidden Markov models, and piecewise smooth filtering are touched on.Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences 11/2011; 467(2135):3115-3140. · 2.38 Impact Factor

Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.