Dennis Trede

Inline hologram reconstruction with sparsity constraints

Inline digital holograms are classically reconstructed using linear operators to model diffraction. It has long been recognized that such reconstruction operators do not invert the hologram formation operator. Classical linear reconstructions yield images with artifacts such as distortions near the field-of-view boundaries or twin images. When objects located at different depths are reconstructed from a hologram, in-focus and out-of-focus images of all objects superimpose upon each other. Additional processing, such as maximum-of-focus detection, is thus unavoidable for any successful use of the reconstructed volume. In this Letter, we consider inverting the hologram formation model in a Bayesian framework. We suggest the use of a sparsity-promoting prior, verified in many inline holography applications, and present a simple iterative algorithm for 3D object reconstruction under sparsity and positivity constraints. Preliminary results with both simulated and experimental holograms are highly promising.

Greedy solution of ill-posed problems: error bounds and exact inversion

The orthogonal matching pursuit (OMP) is a greedy algorithm to solve sparse approximation problems. Sufficient conditions for exact recovery are known with and without noise. In this paper we investigate the applicability of the OMP for the solution of ill-posed inverse problems in general, and in particular for two deconvolution examples from mass spectrometry and digital holography, respectively. In sparse approximation problems one often has to deal with the problem of redundancy of a dictionary, i.e. the atoms are not linearly independent. However, one expects them to be approximatively orthogonal and this is quantified by the so-called incoherence. This idea cannot be transferred to ill-posed inverse problems since here the atoms are typically far from orthogonal. The ill-posedness of the operator probably causes the correlation of two distinct atoms to become huge, i.e. that two atoms look much alike. Therefore, one needs conditions which take the structure of the problem into account and work without the concept of coherence. In this paper we develop results for the exact recovery of the support of noisy signals. In the two examples, mass spectrometry and digital holography, we show that our results lead to practically relevant estimates such that one may check a priori if the experimental setup guarantees exact deconvolution with OMP. Especially in the example from digital holography, our analysis may be regarded as a first step to calculate the resolution power of droplet holography.

Exploring Three-Dimensional Matrix-Assisted Laser Desorption/Ionization Imaging Mass Spectrometry Data: Three-Dimensional Spatial Segmentation of Mouse Kidney

Three-dimensional (3D) imaging has a significant impact on many challenges of life sciences. Three-dimensional matrix-assisted laser desorption/ionization imaging mass spectrometry (MALDI-IMS) is an emerging label-free bioanalytical technique capturing the spatial distribution of hundreds of molecular compounds in 3D by providing a MALDI mass spectrum for each spatial point of a 3D sample. Currently, 3D MALDI-IMS cannot tap its full potential due to the lack efficient computational methods for constructing, processing, and visualizing large and complex 3D MALDI-IMS data. We present a new pipeline of efficient computational methods, which enables analysis and interpretation of a 3D MALDI-IMS data set. Construction of a MALDI-IMS data set was done according to the state-of-the-art protocols and involved sample preparation, spectra acquisition, spectra preprocessing, and registration of serial sections. For analysis and interpretation of 3D MALDI-IMS data, we applied the spatial segmentation approach which is well-accepted in analysis of two-dimensional (2D) MALDI-IMS data. In line with 2D data analysis, we used edge-preserving 3D image denoising prior to segmentation to reduce strong and chaotic spectrum-to-spectrum variation. For segmentation, we used an efficient clustering method, called bisecting k-means, which is optimized for hierarchical clustering of a large 3D MALDI-IMS data set. Using the proposed pipeline, we analyzed a central part of a mouse kidney using 33 serial sections of 3.5 μm thickness after the PAXgene tissue fixation and paraffin embedding. For each serial section, a 2D MALDI-IMS data set was acquired following the standard protocols with the high spatial resolution of 50 μm. Altogether, 512 495 mass spectra were acquired that corresponds to approximately 50 gigabytes of data. After registration of serial sections into a 3D data set, our computational pipeline allowed us to reveal the 3D kidney anatomical structure based on mass spectrometry data only. Finally, automated analysis discovered molecular masses colocalized with major anatomical regions. In the same way, the proposed pipeline can be used for analysis and interpretation of any 3D MALDI-IMS data set in particular of pathological cases.

MALDI mass spectrometric imaging based identification of clinically relevant signals in prostate cancer using large-scale tissue microarrays.

To identify molecular features associated with clinico‐pathological parameters and TMPRSS2‐ERG fusion status in prostate cancer, we employed MALDI mass spectrometric imaging (MSI) to a prostate cancer tissue microarray (TMA) containing formalin‐fixed, paraffin‐embedded tissues samples from 1,044 patients for which clinical follow‐up data were available. MSI analysis revealed 15 distinct mass per charge (m/z)‐signals associated to epithelial structures. A comparison of these signals with clinico‐pathological features revealed statistical association with favorable tumor phenotype such as low Gleason grade, early pT stage or low Ki67 labeling Index (LI) for four signals (m/z 700, m/z 1,502, m/z 1,199 and m/z 3,577), a link between high Ki67LI for one signal (m/z 1,013) and a relationship with prolonged time to PSA recurrence for one signal (m/z 1,502; p = 0.0145). Multiple signals were associated with the ERG‐fusion status of our cancers. Two of 15 epithelium‐associated signals including m/z 1,013 and m/z 1,502 were associated with detectable ERG expression and five signals (m/z 644, 678, 1,044, 3,086 and 3,577) were associated with ERG negativity. These observations are in line with substantial molecular differences between fusion‐type and non‐fusion type prostate cancer. The signals observed in this study may characterize molecules that play a role in the development of TMPRSS2‐ERG fusions, or alternatively reflect pathways that are activated as a consequence of ERG‐activation. The combination of MSI and large‐scale TMAs reflects a powerful approach enabling immediate prioritization of MSI signals based on associations with clinico‐pathological and molecular data.

2D and 3D MALDI-imaging: conceptual strategies for visualization and data mining.

3D imaging has a significant impact on many challenges in life sciences, because biology is a 3-dimensional phenomenon. Current 3D imaging-technologies (various types MRI, PET, SPECT) are labeled, i.e. they trace the localization of a specific compound in the body. In contrast, 3D MALDI mass spectrometry-imaging (MALDI-MSI) is a label-free method imaging the spatial distribution of molecular compounds. It complements 3D imaging labeled methods, immunohistochemistry, and genetics-based methods. However, 3D MALDI-MSI cannot tap its full potential due to the lack of statistical methods for analysis and interpretation of large and complex 3D datasets. To overcome this, we established a complete and robust 3D MALDI-MSI pipeline combined with efficient computational data analysis methods for 3D edge preserving image denoising, 3D spatial segmentation as well as finding colocalized m/z values, which will be reviewed here in detail. Furthermore, we explain, why the integration and correlation of the MALDI imaging data with other imaging modalities allows to enhance the interpretation of the molecular data and provides visualization of molecular patterns that may otherwise not be apparent. Therefore, a 3D data acquisition workflow is described generating a set of 3 different dimensional images representing the same anatomies. First, an in-vitro MRI measurement is performed which results in a three-dimensional image modality representing the 3D structure of the measured object. After sectioning the 3D object into N consecutive slices, all N slices are scanned using an optical digital scanner, enabling for performing the MS measurements. Scanning the individual sections results into low-resolution images, which define the base coordinate system for the whole pipeline. The scanned images conclude the information from the spatial (MRI) and the mass spectrometric (MALDI-MSI) dimension and are used for the spatial three-dimensional reconstruction of the object performed by image registration techniques. Different strategies for automatic serial image registration applied to MS datasets are outlined in detail. The third image modality is histology driven, i.e. a digital scan of the histological stained slices in high-resolution. After fusion of reconstructed scan images and MRI the slice-related coordinates of the mass spectra can be propagated into 3D-space. After image registration of scan images and histological stained images, the anatomical information from histology is fused with the mass spectra from MALDI-MSI. As a result of the described pipeline we have a set of 3 dimensional images representing the same anatomies, i.e. the reconstructed slice scans, the spectral images as well as corresponding clustering results, and the acquired MRI. Great emphasis is put on the fact that the co-registered MRI providing anatomical details improves the interpretation of 3D MALDI images. The ability to relate mass spectrometry derived molecular information with in vivo and in vitro imaging has potentially important implications. This article is part of a Special Issue entitled: Computational Proteomics in the Post-Identification Era. Guest Editors: Martin Eisenacher and Christian Stephan.

MRI-compatible pipeline for three-dimensional MALDI imaging mass spectrometry using PAXgene fixation

UNLABELLED MALDI imaging mass spectrometry (MALDI-imaging) has emerged as a spatially-resolved label-free bioanalytical technique for direct analysis of biological samples and was recently introduced for analysis of 3D tissue specimens. We present a new experimental and computational pipeline for molecular analysis of tissue specimens which integrates 3D MALDI-imaging, magnetic resonance imaging (MRI), and histological staining and microscopy, and evaluate the pipeline by applying it to analysis of a mouse kidney. To ensure sample integrity and reproducible sectioning, we utilized the PAXgene fixation and paraffin embedding and proved its compatibility with MRI. Altogether, 122 serial sections of the kidney were analyzed using MALDI-imaging, resulting in a 3D dataset of 200GB comprised of 2million spectra. We show that elastic image registration better compensates for local distortions of tissue sections. The computational analysis of 3D MALDI-imaging data was performed using our spatial segmentation pipeline which determines regions of distinct molecular composition and finds m/z-values co-localized with these regions. For facilitated interpretation of 3D distribution of ions, we evaluated isosurfaces providing simplified visualization. We present the data in a multimodal fashion combining 3D MALDI-imaging with the MRI volume rendering and with light microscopic images of histologically stained sections. BIOLOGICAL SIGNIFICANCE Our novel experimental and computational pipeline for 3D MALDI-imaging can be applied to address clinical questions such as proteomic analysis of the tumor morphologic heterogeneity. Examining the protein distribution as well as the drug distribution throughout an entire tumor using our pipeline will facilitate understanding of the molecular mechanisms of carcinogenesis.

Beyond convergence rates: exact recovery with the Tikhonov regularization with sparsity constraints

The Tikhonov regularization of linear ill-posed problems with an l1 penalty is considered. We recall results for linear convergence rates and results on exact recovery of the support. Moreover, we derive conditions for exact support recovery which are especially applicable in the case of ill-posed problems, where other conditions, e.g., based on the so-called coherence or the restricted isometry property are usually not applicable. The obtained results also show that the regularized solutions do not only converge in the l1-norm but also in the vector space l0 (when considered as the strict inductive limit of the spaces as n tends to infinity). Additionally, the relations between different conditions for exact support recovery and linear convergence rates are investigated. With an imaging example from digital holography the applicability of the obtained results is illustrated, i.e. that one may check a priori if the experimental setup guarantees exact recovery with the Tikhonov regularization with sparsity constraints.

Benchmark datasets for 3D MALDI- and DESI-imaging mass spectrometry

BackgroundThree-dimensional (3D) imaging mass spectrometry (MS) is an analytical chemistry technique for the 3D molecular analysis of a tissue specimen, entire organ, or microbial colonies on an agar plate. 3D-imaging MS has unique advantages over existing 3D imaging techniques, offers novel perspectives for understanding the spatial organization of biological processes, and has growing potential to be introduced into routine use in both biology and medicine. Owing to the sheer quantity of data generated, the visualization, analysis, and interpretation of 3D imaging MS data remain a significant challenge. Bioinformatics research in this field is hampered by the lack of publicly available benchmark datasets needed to evaluate and compare algorithms.FindingsHigh-quality 3D imaging MS datasets from different biological systems at several labs were acquired, supplied with overview images and scripts demonstrating how to read them, and deposited into MetaboLights, an open repository for metabolomics data. 3D imaging MS data were collected from five samples using two types of 3D imaging MS. 3D matrix-assisted laser desorption/ionization imaging (MALDI) MS data were collected from murine pancreas, murine kidney, human oral squamous cell carcinoma, and interacting microbial colonies cultured in Petri dishes. 3D desorption electrospray ionization (DESI) imaging MS data were collected from a human colorectal adenocarcinoma.ConclusionsWith the aim to stimulate computational research in the field of computational 3D imaging MS, selected high-quality 3D imaging MS datasets are provided that could be used by algorithm developers as benchmark datasets.

On the Importance of Mathematical Methods for Analysis of MALDI-Imaging Mass Spectrometry Data

In the last decade, matrix-assisted laser desorption/ionization (MALDI) imaging mass spectrometry (IMS), also called as MALDI-imaging, has proven its potential in proteomics and was successfully applied to various types of biomedical problems, in particular to histopathological label-free analysis of tissue sections. In histopathology, MALDI-imaging is used as a general analytic tool revealing the functional proteomic structure of tissue sections, and as a discovery tool for detecting new biomarkers discriminating a region annotated by an experienced histologist, in particular, for cancer studies. A typical MALDI-imaging data set contains 10⁸ to 10⁹ intensity values occupying more than 1 GB. Analysis and interpretation of such huge amount of data is a mathematically, statistically and computationally challenging problem. In this paper we overview some computational methods for analysis of MALDI-imaging data sets. We discuss the importance of data preprocessing, which typically includes normalization, baseline removal and peak picking, and hightlight the importance of image denoising when visualizing IMS data.

Spatial Segmentation of MALDI FT-ICR MSI Data: A Powerful Tool to Explore the Head and Neck Tumor In Situ Lipidome

AbstractMatrix-assisted laser desorption/ionization mass spectrometric imaging (MALDI MSI) is a well-established analytical technique for determining spatial localization of lipids in biological samples. The use of Fourier-transform ion cyclotron resonance (FT-ICR) mass spectrometers for the molecular imaging of endogenous compounds is gaining popularity, since the high mass accuracy and high mass resolving power enables accurate determination of exact masses and, consequently, a more confident identification of these molecules. The high mass resolution FT-ICR imaging datasets are typically large in size. In order to analyze them in an appropriate timeframe, the following approach has been employed: the FT-ICR imaging datasets were spatially segmented by clustering all spectra by their similarity. The resulted spatial segmentation maps were compared with the histologic annotation. This approach facilitates interpretation of the full datasets by providing spatial regions of interest. The application of this approach, which has originally been developed for MALDI-TOF MSI datasets, to the lipidomic analysis of head and neck tumor tissue revealed new insights into the metabolic organization of the carcinoma tissue. Graphical Abstractᅟ