Splines in Higher Order TV Regularization

By Gabriele Steidl, Stephan Didas, Julia Neumann. 2006

88 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mathematical Physics, Mechanics of Materials

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Citations in the corpus

Additive models with trend filtering (2017, methodology): “This intuition is formalized in Tibshirani (2014) and Wang et al. (2014), where it is shown that the components of the kth order trend filtering estimate θ̂ are precisely the evaluations of a fitted kth order piecewise polynomial function across the inputs, and that the trend filtering and locally a”
Exact post-selection inference for the generalized lasso path (2018, background): “Trend ﬁltering can be seen as an extension of the 1d fused lasso for ﬁtting higher-order piecewise polynomials [32, 21, 35].”
A Direct Algorithm for 1-D Total Variation Denoising (2013, methodology): “Future work will include the extension of the algorithm to generalized forms of the TV, where the two-tap ﬁnite difference is replaced by another discrete differential operator, to favor piecewise polynomial reconstruction of higher degree or other types of signals [33], [35].”
The Generalized Lasso Problem and Uniqueness (2018, background): “1 in Tibshirani and Taylor (2011)); (iii) D ∈ R(p−k−1)×p is the (k + 1)st order difference matrix, i.e., kth order trend filtering penalty matrix (see Section 2.1.2 in Tibshirani and Taylor (2011)), and n ≥ k + 1; (iv) D ∈ Rm×p is the graph fused lasso penalty matrix, defined over a graph with m edg”
Fast and Flexible ADMM Algorithms for Trend Filtering (2014, methodology): “Trend ﬁltering is a relatively new method for nonparametric regression, proposed independently by Steidl et al. (2006) and Kim et al. (2009).”