Regularization methods for linear inverse problems

Solutions of Ill-Posed Problems.

1978 • 8,291 citations

Smoothing noisy data with spline functions

1978 • 3,289 citations

Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - I

1961 • 2,466 citations

Introduction to the theory of Fourier integrals

1937 • 2,362 citations

Solution of incorrectly formulated problems and the regularization method

1963 • 2,355 citations

Smoothing by spline functions

1967 • 2,217 citations

Lectures on Cauchy's Problem in Linear Partial Differential Equations

1953 • 2,155 citations

Image reconstruction from projections : the fundamentals of computerized tomography

1980 • 2,055 citations

A Technique for the Numerical Solution of Certain Integral Equations of the First Kind

1962 • 2,001 citations

The Resolving Power of Gross Earth Data

1968 • 1,467 citations

Methods for Solving Incorrectly Posed Problems

1984 • 1,322 citations

The theory of Tikhonov regularization for Fredholm equations of the first kind

1984 • 1,219 citations

An Iteration Formula for Fredholm Integral Equations of the First Kind

1951 • 1,056 citations

Inverse Problems in Quantum Scattering Theory

1977 • 1,050 citations

REGULARIZATION OF INCORRECTLY POSED PROBLEMS

1963 • 890 citations

Practical Approximate Solutions to Linear Operator Equations When the Data are Noisy

1977 • 777 citations

Systems and transforms with applications in optics

1969 • 739 citations

Systems and transforms with applications in optics

1968 • 607 citations

Well-posed stochastic extensions of ill-posed linear problems

1970 • 560 citations

Least Squares Methods for Ill-Posed Problems with a Prescribed Bound

1970 • 502 citations

Theory and applications of spline functions

1969 • 393 citations

Improperly Posed Problems in Partial Differential Equations

1975 • 344 citations

Continuous dependence on data for solutions of partial differential equations with a prescribed bound

1960 • 300 citations

Some Improperly Posed Problems of Mathematical Physics

1967 • 288 citations

A Collection of Matrices for Testing Computational Algorithms

1971 • 269 citations

Linear inverse problems with discrete data. I. General formulation and singular system analysis

1985 • 243 citations

Some Improperly Posed Problems of Mathematical Physics

1967 • 195 citations

Generalized inverses of linear operators

1977 • 185 citations

Picture Processing and Digital Filtering

1975 • 184 citations

Inverse Source Problems in Optics

1978 • 167 citations

Inverse Scattering Problems in Optics

1980 • 157 citations

On the Convergence of the Conjugate Gradient Method for Singular Linear Operator Equations

1972 • 151 citations

Analytic extrapolation techniques and stability problems in dispersion relation theory

1975 • 132 citations

On the characteristic values of linear integral equations

1931 • 125 citations

Mathematical problems of computerized tomography

1983 • 124 citations

Applied Inverse Problems

1978 • 119 citations

Finite element approximation of regularized solutions of the inverse potential problem of electrocardiography and applications to experimental data

1985 • 117 citations

The error principle in the solution of operational equations by the regularization method

1968 • 103 citations

Inverse Methods in Electromagnetic Imaging

1985 • 96 citations

Spectral approach to geophysical inversion by Lorentz, Fourier, and Radon transforms

1982 • 94 citations

On Tikhonov’s method for ill-posed problems

1974 • 76 citations

Numerical solution of the equation of heat conduction for preceding times

1955 • 72 citations

Formulation of some Improperly Posed Problems of Mathematical Physics

1967 • 57 citations

On moment-discretization and least-squares solutions of linear integral equations of the first kind

1976 • 56 citations

The Dirichlet problem for the wave equation

1958 • 54 citations

Sur un thÉorÈme gÉnÉral relatif aux Équations intÉgrales de premiÈre espÈce et sur quelques problÈmes de physique mathÉmatique

1910 • 47 citations

Three circle theorems in partial differential equations and applications to improperly posed problems

1964 • 47 citations

The approximate solution of operator equations of the first kind

1966 • 42 citations

Experimental Determination of Temperature Profiles by Ground-Based Microwave Radiometry

1975 • 39 citations

Steepest descent for singular linear operators with nonclosed range

1971 • 35 citations

Improperly Posed Boundary Value Problems

1976 • 34 citations

A numerical method for solving Fredholm integral equations of the 1st kind

1965 • 22 citations

ON PROBABILISTIC METHODS FOR THE SOLUTION OF IMPROPERLY POSED PROBLEMS

1978 • 12 citations