27 citations · 138 across the 24 of their papers we have counts for
28 papers
Relaxations for Non-Separable Cardinality/Rank Penalties
Carl Olsson, Daniele Gerosa, Marcus Carlsson
Rank and cardinality penalties are hard to handle in optimization frameworks due to non-convexity and discontinuity. Strong approximations have been a subject of intense study and…
Numerical simulations of NMR relaxation in chalk using local Robin boundary conditions
M. Ogren, D. Jha, S. Dobberschutz +5
The interpretation of nuclear magnetic resonance (NMR) data is of interest in a number of fields. In Ögren [Eur. Phys. J. B (2014) 87: 255] local boundary conditions for random wal…
An unbiased approach to low rank recovery
Marcus Carlsson, Daniele Gerosa, Carl Olsson
Low rank recovery problems have been a subject of intense study in recent years. While the rank function is useful for regularization it is difficult to optimize due to its non-con…
On phase retrieval via matrix completion and the estimation of low rank PSD matrices
Marcus Carlsson, Daniele Gerosa
Given underdetermined measurements of a Positive Semi-Definite (PSD) matrix of known low rank , we present a new algorithm to estimate based on recent advances in non-co…
Bias Reduction in Compressed Sensing
Carl Olsson, Marcus Carlsson, Daniele Gerosa
Sparsity and rank functions are important ways of regularizing under-determined linear systems. Optimization of the resulting formulations is made difficult since both these penalt…
On Convex Envelopes and Regularization of Non-Convex Functionals without moving Global Minima
Marcus Carlsson
We provide theory for the computation of convex envelopes of non-convex functionals including an l2-term, and use these to suggest a method for regularizing a more general set of p…
Perturbation theory for Hermitian matrix-functions based on vector-fields
Marcus Carlsson
We consider "spectral" matrix-functions for Hermitian matrices, where the novelty is that the function applied to the spectrum is allowed to be a vector-field rather than a scalar…
Perturbation theory for the matrix square root and matrix modulus
Marcus Carlsson
We provide first order perturbation formulas for the matrix square root (in the positive semi-definite case) and the matrix modulus (in the general case). The results are new for s…
Four-dimensional tomographic reconstruction by time domain decomposition
Viktor V. Nikitin, Marcus Carlsson, Fredrik Andersson +1
Since the beginnings of tomography, the requirement that the sample does not change during the acquisition of one tomographic rotation is unchanged. We derived and successfully imp…
Perturbation theory for the spectral decomposition of Hermitian matrices
Marcus Carlsson
Let A and E be Hermitian self-adjoint matrices, where A is fixed and E a small perturbation. We study how the eigenvalues and eigenvectors of A+E depend on E, with the aim of obtai…
An unbiased approach to compressed sensing
Marcus Carlsson, Daniele Gerosa, Carl Olsson
In compressed sensing a sparse vector is approximately retrieved from an under-determined equation system . Exact retrieval would mean solving a large combinatorial problem w…
Nehari's theorem for convex domain Hankel and Toeplitz operators in several variables
Marcus Carlsson, Karl-Mikael Perfekt
We prove Nehari's theorem for integral Hankel and Toeplitz operators on simple convex polytopes in several variables. A special case of the theorem, generalizing the boundedness cr…
A Non-Convex Relaxation for Fixed-Rank Approximation
Carl Olsson, Marcus Carlsson, Erik Bylow
This paper considers the problem of finding a low rank matrix from observations of linear combinations of its elements. It is well known that if the problem fulfills a restricted i…
ESPRIT for multidimensional general grids
Fredrik Andersson, Marcus Carlsson
We present a new method for complex frequency estimation in several variables, extending the classical (1d) ESPRIT-algorithm. We also consider how to work with data sampled on non-…
Non-Convex Rank/Sparsity Regularization and Local Minima
Carl Olsson, Marcus Carlsson, Fredrik Andersson +1
This paper considers the problem of recovering either a low rank matrix or a sparse vector from observations of linear combinations of the vector or matrix elements. Recent methods…
Convergence of dual ascent in non-convex/non-differentiable optimization
Fredrik Andersson, Marcus Carlsson, Carl Olsson
We revisit the classical dual ascent algorithm for minimization of convex functionals in the presence of linear constraints, and give convergence results which apply even for non-c…
On convexification/optimization of functionals including an l2-misfit term
Marcus Carlsson
We provide theory for computing the lower semi-continuous convex envelope of functionals of the type f(x) plus an l2 misfit, and discuss applications to various non-convex optimiza…
Convex envelopes for fixed rank approximation
Fredrik Andersson, Marcus Carlsson, Carl Olsson
A convex envelope for the problem of finding the best approximation to a given matrix with a prescribed rank is constructed. This convex envelope allows the usage of traditional op…
Fast hyperbolic Radon transform represented as convolutions in log-polar coordinates
Viktor V. Nikitin, Fredrik Andersson, Marcus Carlsson +1
The hyperbolic Radon transform is a commonly used tool in seismic processing, for instance in seismic velocity analysis, data interpolation and for multiple removal. A direct imple…
Fixed-point algorithms for frequency estimation and structured low rank approximation
Fredrik Andersson, Marcus Carlsson
We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by s…
On the Kronecker and Caratheodory-Fejer theorems in several variables
Fredrik Andersson, Marcus Carlsson
Multivariate versions of the Kronecker theorem in the continuous multivariate setting has recently been published. These theorems characterize the symbols that give rise to finite…
Fast algorithms and efficient GPU implementations for the Radon transform and the back-projection operator represented as convolution operators
Fredrik Andersson, Marcus Carlsson, Viktor V. Nikitin
The Radon transform and its adjoint, the back-projection operator, can both be expressed as convolutions in log-polar coordinates. Hence, fast algorithms for the application of the…
Operator-Lipschitz estimates for the singular value functional calculus
Fredrik Andersson, Marcus Carlsson, Karl-Mikael Perfekt
We consider a functional calculus for compact operators, acting on the singular values rather than the spectrum, which appears frequently in applied mathematics. Necessary and suff…
On linear differential equations with infinitely many derivatives
Marcus Carlsson, Humberto Prado, Enrique G. Reyes
Differential equations with infinitely many derivatives, sometimes also referred to as ``nonlocal'' differential equations, appear frequently in branches of modern physics such as…