Local Strong Homogeneity of a Regularized Estimator

By Mila Nikolova. SIAM Journal on Applied Mathematics, 2000

312 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ed75248998fb1ac44026b1013e0d6e6593d2c150

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Citations in the corpus

SparseNet: Coordinate Descent With Nonconvex Penalties (2011, background): “Other examples of nonconvex penalties include the transformed 1 penalty (Nikolova 2000) and the clipped 1 penalty (Zhang 2010b).”
A unified approach to model selection and sparse recovery using regularized least squares (2009, background): “Nikolova (2000) studies the transformed L 1 penalty function ρ ( t ) = bt/ (1+ bt ), t ∈ [0 , ∞ ) and b > 0.”
Edge-preserving and scale-dependent properties of total variation regularization (2003, background): “(This staircasing effect is well known and is currently being studied [5, 9, 11, 29, 32].”
Recovering Sparse Signals With a Certain Family of Nonconvex Penalties and DC Programming (2009, unknown): “For these purposes, they advocate that penalty functions should be singular at the origin for achieving sparsity (the same argument was also developed in [2], [32]) and should be such that their derivatives vanish for large values.”
Inpainting and Zooming Using Sparse Representations (2009, background): “Minimizers of Equation (6) for a general class of regularizing functions (neither non-necessarily differentiable nor convex) have been characterized in a rigorous and systematic way for the orthogonal wavelet transform in [52], and general F in [53].”
Model distortions in Bayesian MAP reconstruction (2007, background): “The observed incoherence between the models fX and fY|X on the one hand, and the estimator X̂ on the other hand, is inherent since it originates from the analytical properties of the MAP solution corresponding to nonsmooth prior energies combined with smooth data-acquisition models [42, 46].”
Regularization of Wavelet Approximations (2001, methodology): “A possible method is to apply the graduated nonconvexity (GNC) algorithm introduced by Blake and Zisserman (1987) and Blake (1989) and ameliorated by Nikolova (1999) and Nikolova, Idier, and Mohammad-Djafari (in press) in the imaging analysis context.”
Sure independence screening for ultrahigh dimensional feature space (2006, methodology): “P ( n(ξ1 + · · ·+ ξn) < 1− ε ) ≤ eε, (48)”
Split Bregman Methods and Frame Based Image Restoration (2009, background): “For example, the l1 norm term yields a solution with large strongly homogeneous zones, as shown in [55, 56].”
Analysis of Half-Quadratic Minimization Methods for Signal and Image Recovery (2005, background): “25) near 0 allows smoothly varying regions in x̂ to be restored [25].”
Image restoration: Total variation, wavelet frames, and beyond (2012, background): “However, it will also create the staircase effect for images that are not piecewise constant [24, 25].”