Automated Co-Analysis of MALDI and H&amp;E Images of Retinal Tissue for an Improved Spatial MALDI Resolution

Schönmeyer, Ralf; Schmidt, Günter; Meding, Stephan; Walch, Axel; Binnig, G.

doi:10.1007/978-3-642-36480-8_39

Cited by 2 publications

(3 citation statements)

References 5 publications

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“…We apply the proposed iPotts-ADMM algorithm to reconstruct jump-sparse signals, which arise in various applications such as stepping rotations of bacterial flagella [35], the crosshybridization of DNA [36], [37], [38], single-molecule fluorescence resonance energy transfer [39], and MALDI imaging [40]. Here, we recover jump-sparse signals from indirect measurements, for example from blurred data or Fourier data.…”

Section: Applications and Numerical Experimentsmentioning

confidence: 99%

Jump-Sparse and Sparse Recovery Using Potts Functionals

Storath

Weinmann

Demaret

2014

IEEE Trans. Signal Process.

100

101

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Abstract-We recover jump-sparse and sparse signals from blurred incomplete data corrupted by (possibly non-Gaussian) noise using inverse Potts energy functionals. We obtain analytical results (existence of minimizers, complexity) on inverse Potts functionals and provide relations to sparsity problems. We then propose a new optimization method for these functionals which is based on dynamic programming and the alternating direction method of multipliers (ADMM). A series of experiments shows that the proposed method yields very satisfactory jumpsparse and sparse reconstructions, respectively. We highlight the capability of the method by comparing it with classical and recent approaches such as TV minimization (jump-sparse signals), orthogonal matching pursuit, iterative hard thresholding, and iteratively reweighted 1 minimization (sparse signals).

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Section: Applications and Numerical Experimentsmentioning

confidence: 99%

Jump-Sparse and Sparse Recovery Using Potts Functionals

Storath

Weinmann

Demaret

2014

IEEE Trans. Signal Process.

100

101

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“…Recovery of piecewise constant signals from corrupted data is a task needed in various fields of applied sciences. Examples are the reconstruction of brain stimuli [28], the cross-hybridization of DNA [13,19] and MALDI imaging [26]. The data may be incomplete frequency information as in [7,22] or noisy and blurred measurements as in this paper.…”

Section: Introductionmentioning

confidence: 99%

“…This statement is formulated as Theorem 3.3 which, more generally, treats the case of not necessarily equal weights. Such weights arise naturally in applications where data are available only on a non-uniform grid [26]. The key to the speed-up is to work with dynamic data structures tailored to the problem.…”

Section: Introductionmentioning

confidence: 99%

The $L^1$-Potts Functional for Robust Jump-Sparse Reconstruction

Weinmann

Storath²,

Demaret³

2015

SIAM J. Numer. Anal.

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Abstract. We investigate the non-smooth and non-convex L 1 -Potts functional in discrete and continuous time. We show Γ-convergence of discrete L 1 -Potts functionals towards their continuous counterpart and obtain a convergence statement for the corresponding minimizers as the discretization gets finer. For the discrete L 1 -Potts problem, we introduce an O(n 2 ) time and O(n) space algorithm to compute an exact minimizer. We apply L 1 -Potts minimization to the problem of recovering piecewise constant signals from noisy measurements f. It turns out that the L 1 -Potts functional has a quite interesting blind deconvolution property. In fact, we show that mildly blurred jump-sparse signals are reconstructed by minimizing the L 1 -Potts functional. Furthermore, for strongly blurred signals and known blurring operator, we derive an iterative reconstruction algorithm.

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Automated Co-Analysis of MALDI and H&E Images of Retinal Tissue for an Improved Spatial MALDI Resolution

Cited by 2 publications

References 5 publications

Jump-Sparse and Sparse Recovery Using Potts Functionals

Jump-Sparse and Sparse Recovery Using Potts Functionals

The $L^1$-Potts Functional for Robust Jump-Sparse Reconstruction

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