Journal Article10.1190/1.1440378
Robust Modeling With Erratic Data
Jon F. Claerbout,Francis Muir +1 more
874
TL;DR: An alternative to least-squares data modeling techniques is the use of absolute value error criteria as discussed by the authors, where the inclusion of some infinite blunders along with the data will hardly affect the solution to an otherwise well-posed problem.
read more
Abstract: An attractive alternative to least‐squares data modeling techniques is the use of absolute value error criteria. Unlike the least‐squares techniques the inclusion of some infinite blunders along with the data will hardly affect the solution to an otherwise well‐posed problem. An example of this great stability is seen when an average is, determined by using the median rather than the arithmetic mean. Algorithms for absolute error minimization are often approximately as costly as least‐squares algorithms; however, unlike least‐squares, they naturally lend themselves to inequality or bounding constraints on models.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
•Book
Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers
Stephen Boyd,Neal Parikh,Eric Chu,Borja Peleato,Jonathan Eckstein +4 more
- 23 May 2011
TL;DR: It is argued that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas.
An Introduction To Compressive Sampling
TL;DR: The theory of compressive sampling, also known as compressed sensing or CS, is surveyed, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisition.
11.2K
Enhancing Sparsity by Reweighted ℓ 1 Minimization
TL;DR: A novel method for sparse signal recovery that in many situations outperforms ℓ1 minimization in the sense that substantially fewer measurements are needed for exact recovery.
Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
TL;DR: It is shown that if a certain restricted isometry property holds for the linear transformation defining the constraints, the minimum-rank solution can be recovered by solving a convex optimization problem, namely, the minimization of the nuclear norm over the given affine space.
4.4K
Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems
TL;DR: This paper proposes gradient projection algorithms for the bound-constrained quadratic programming (BCQP) formulation of these problems and test variants of this approach that select the line search parameters in different ways, including techniques based on the Barzilai-Borwein method.
References
Numerical Applications of a Formalism for Geophysical Inverse Problems
George E. Backus,J. F. Gilbert +1 more
TL;DR: In this paper, the authors prove that the collection of Earth models which yield the physically observed values of any independent set of gross Earth data is either empty or infinite dimensional, and exploit this very high degree of non-uniqueness in real geophysical inverse problems to generate computer programs which iteratively produce Earth models to fit given gross earth data and satisfy other criteria.
946
Maximum entropy power spectrum of truncated sinusoids
TL;DR: The frequency shifts observed in the power spectra of truncated sinusoids, when the sinusoid are computed by using the periodogram, are obviated by means of a maximum entropy algorithm as mentioned in this paper.
178
Algorithms for bestL 1 andL ∞ linear approximations on a discrete set
Ian Barrodale,Andrew J. Young +1 more
TL;DR: This paper supplies algorithms for the best approximation to a real-valued function, defined as a table of values, by a linear approximating function in both the L1 and L∞ norms.
132
Studies in the History of Probability and Statistics. XXIX The discovery of the method of least squares
TL;DR: In this paper, the circumstances in which the discovery of the method of least squares took place and the course of the ensuing controversy are examined in detail with the aid of correspondence, drawing conclusions about the attitudes of the main participants and the nature of historical research in statistics.
130
Adaptive Antenna Systems
TL;DR: The techniques described in this paper are applicable to signal‐receiving arrays for use over a wide range of frequencies and substantial reductions in noise reception are demonstrated in computer‐simulated experiments.