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Deep learning (DL) has recently emerged as a pivotal technology for enhancing magnetic resonance imaging (MRI), a critical tool in diagnostic radiology. This review paper provides a comprehensive overview of recent advances in DL for MRI reconstruction, and focuses on various DL approaches and architectures designed to improve image quality, accelerate scans, and address data-related challenges. It explores end-to-end neural networks, pre-trained and generative models, and self-supervised methods, and highlights their contributions to overcoming traditional MRI limitations. It also discusses the role of DL in optimizing acquisition protocols, enhancing robustness against distribution shifts, and tackling biases. Drawing on the extensive literature and practical insights, it outlines current successes, limitations, and future directions for leveraging DL in MRI reconstruction, while emphasizing the potential of DL to significantly impact clinical imaging practices. [ABSTRACT FROM AUTHOR]

Deep neural networks provide state-of-the-art performance for image denoising, where the goal is to recover a near noise-free image from a noisy observation. The underlying principle is that neural networks trained on large data sets have empirically been shown to be able to generate natural images well from a low-dimensional latent representation of the image. Given such a generator network, a noisy image can be denoised by (i) finding the closest image in the range of the generator or by (ii) passing it through an encoder-generator architecture (known as an autoencoder). However, there is little theory to justify this success, let alone to predict the denoising performance as a function of the network parameters. In this paper, we consider the problem of denoising an image from additive Gaussian noise using the two generator-based approaches. In both cases, we assume the image is well described by a deep neural network with ReLU activations functions, mapping a |$k$| -dimensional code to an |$n$| -dimensional image. In the case of the autoencoder, we show that the feedforward network reduces noise energy by a factor of |$O(k/n)$|⁠. In the case of optimizing over the range of a generative model, we state and analyze a simple gradient algorithm that minimizes a non-convex loss function and provably reduces noise energy by a factor of |$O(k/n)$|⁠. We also demonstrate in numerical experiments that this denoising performance is, indeed, achieved by generative priors learned from data. [ABSTRACT FROM AUTHOR]

Due to its longevity and enormous information density, DNA is an attractive medium for archival storage. In this work, we study the fundamental limits and trade-offs of DNA-based storage systems by introducing a new channel model, which we call the noisy shuffling-sampling channel. Motivated by current technological constraints on DNA synthesis and sequencing, this model captures three key distinctive aspects of DNA storage systems: (1) the data is written onto many short DNA molecules; (2) the molecules are corrupted by noise during synthesis and sequencing and (3) the data is read by randomly sampling from the DNA pool. We provide capacity results for this channel under specific noise and sampling assumptions and show that, in many scenarios, a simple index-based coding scheme is optimal. [ABSTRACT FROM AUTHOR]

Today, we can read human genomes and store digital data robustly in synthetic DNA. Herein, we report a strategy to intertwine these two technologies to enable the secure storage of valuable information in synthetic DNA, protected with personalized keys. We show that genetic short tandem repeats (STRs) contain sufficient entropy to generate strong encryption keys, and that only one technology, DNA sequencing, is required to simultaneously read the key and the data. Using this approach, we experimentally generated 80 bit strong keys from human DNA, and used such a key to encrypt 17 kB of digital information stored in synthetic DNA. Finally, the decrypted information was recovered perfectly from a single massively parallel sequencing run. [ABSTRACT FROM AUTHOR]

We consider the problem of generating interpretable recommendations by identifying overlapping co-clusters of clients and products, based only on positive or implicit feedback. Our approach is applicable on very large datasets because it exhibits almost linear complexity in the input examples and the number of co-clusters. We show, both on real industrial data and on publicly available datasets, that the recommendation accuracy of our algorithm is competitive to that of state-of-the-art matrix factorization techniques. In addition, our technique has the advantage of offering recommendations that are textually and visually interpretable. Our formulation can also address cold-start problems by gracefully meshing collaborative and content-based reasoning. Finally, we present efficient Graphical Processing Unit (GPU) implementations and demonstrate a speedup of more than 270 times over our baseline CPU implementation on a cluster of 16 GPUs. [ABSTRACT FROM AUTHOR]

Line spectral estimation is the problem of recovering the frequencies and amplitudes of a mixture of a few sinusoids from equispaced samples. However, in a variety of signal processing problems arising in imaging, radar, and localization, we do not have access directly to such equispaced samples. Rather, we only observe a severely undersampled version of these observations through linear measurements. This paper is about such generalized line spectral estimation problems. We reformulate these problems as sparse signal recovery problems over a continuously indexed dictionary, which can be solved via a convex program. We prove that the frequencies and amplitudes of the components of the mixture can be recovered perfectly from a near-minimal number of observations via this convex program. This result holds provided the frequencies are sufficiently separated, and the linear measurements obey natural conditions that are satisfied in a variety of applications. [ABSTRACT FROM AUTHOR]

Subspace clustering refers to the problem of clustering unlabeled high-dimensional data points into a union of low-dimensional linear subspaces, whose number, orientations and dimensions are all unknown. In practice, one may have access to dimensionality-reduced observations of the data only, resulting, e.g., from undersampling due to complexity and speed constraints on the acquisition device or mechanism. More pertinently, even if the high-dimensional data set is available, it is often desirable to first project the data points into a lower-dimensional space and to perform clustering there; this reduces storage requirements and computational cost. The purpose of this article is to quantify the impact of dimensionality reduction through random projection on the performance of three subspace clustering algorithms, all of which are based on principles from sparse signal recovery. Specifically, we analyze the thresholding based subspace clustering (TSC) algorithm, the sparse subspace clustering (SSC) algorithm and an orthogonal matching pursuit variant thereof (SSC-OMP). We find, for all three algorithms, that dimensionality reduction down to the order of the subspace dimensions is possible without incurring significant performance degradation. Moreover, these results are order-wise optimal in the sense that reducing the dimensionality further leads to a fundamentally ill-posed clustering problem. Our findings carry over to the noisy case as illustrated through analytical results for TSC and simulations for SSC and SSC-OMP. Extensive experiments on synthetic and real data complement our theoretical findings. [ABSTRACT FROM AUTHOR]

The problem of clustering noisy and incompletely observed high-dimensional data points into a union of low-dimensional subspaces and a set of outliers is considered. The number of subspaces, their dimensions, and their orientations are assumed unknown. We propose a simple low-complexity subspace clustering algorithm, which applies spectral clustering to an adjacency matrix obtained by thresholding the correlations between data points. In other words, the adjacency matrix is constructed from the nearest neighbors of each data point in spherical distance. A statistical performance analysis shows that the algorithm exhibits robustness to additive noise and succeeds even when the subspaces intersect. Specifically, our results reveal an explicit tradeoff between the affinity of the subspaces and the tolerable noise level. We furthermore prove that the algorithm succeeds even when the data points are incompletely observed with the number of missing entries allowed to be (up to a log-factor) linear in the ambient dimension. We also propose a simple scheme that provably detects outliers, and we present numerical results on real and synthetic data. [ABSTRACT FROM PUBLISHER]

Auf Papier gedruckte oder auf Mikrofilm projizierte Information kann mehr als 500 Jahre überdauern. Die Speicherung von digitaler Information über Zeiträume über 50 Jahre stellt hingegen eine große Herausforderung dar. Hier zeigen wir, dass digitale Information auf DNA gespeichert werden kann und auch nach wesentlich längeren Zeiträumen wieder fehlerfrei auslesbar ist. Um eine Wiederherstellung der gespeicherten Information zu gewährleisten, wurde DNA in eine anorganische Matrix eingeschlossen. Zusätzlich dazu wurden fehlerkorrigierende Codes verwendet, um während der Lagerung entstehende Fehler zu beheben. Hierfür codierten wir 83 Kilobytes an Information in 4991 DNA-Segmente, die jeweils 158 Nukleotide lang waren und in einer SiO2-Matrix eingeschlossen wurden. Beschleunigte Alterungsprozesse wurden simuliert, um die Zerfallskinetik der DNA zu untersuchen. Es zeigte sich, dass die Daten in DNA unter verschiedensten Bedingungen Jahrhunderte lang archiviert werden können. Die ursprüngliche Information konnte selbst nach einwöchiger Lagerung bei 70 °C noch fehlerfrei wiederhergestellt werden. Dies ist thermisch äquivalent zu einer Lagerung in Zentraleuropa über einem Zeitraum von ca. 2000 Jahren. [ABSTRACT FROM AUTHOR]

Information, such as text printed on paper or images projected onto microfilm, can survive for over 500 years. However, the storage of digital information for time frames exceeding 50 years is challenging. Here we show that digital information can be stored on DNA and recovered without errors for considerably longer time frames. To allow for the perfect recovery of the information, we encapsulate the DNA in an inorganic matrix, and employ error-correcting codes to correct storage-related errors. Specifically, we translated 83 kB of information to 4991 DNA segments, each 158 nucleotides long, which were encapsulated in silica. Accelerated aging experiments were performed to measure DNA decay kinetics, which show that data can be archived on DNA for millennia under a wide range of conditions. The original information could be recovered error free, even after treating the DNA in silica at 70 °C for one week. This is thermally equivalent to storing information on DNA in central Europe for 2000 years. [ABSTRACT FROM AUTHOR]

We consider the problem of identifying a linear deterministic operator from its response to a given probing signal. For a large class of linear operators, we show that stable identifiability is possible if the total support area of the operator's spreading function satisfies \Delta \leq 1/ 2. This result holds for an arbitrary (possibly fragmented) support region of the spreading function, does not impose limitations on the total extent of the support region, and, most importantly, does not require the support region to be known prior to identification. Furthermore, we prove that stable identifiability of almost all operators is possible if \Delta < 1. This result is surprising as it says that there is no penalty for not knowing the support region of the spreading function prior to identification. Algorithms that provably recover all operators with \Delta \leq 1/ 2, and almost all operators with \Delta < 1 are presented. [ABSTRACT FROM PUBLISHER]

Nested canalizing Boolean functions (NCF) play an important role in biologically motivated regulatory networks and in signal processing, in particular describing stack filters. It has been conjectured that NCFs have a stabilizing effect on the network dynamics. It is well known that the average sensitivity plays a central role for the stability of (random) Boolean networks. Here we provide a tight upper bound on the average sensitivity of NCFs as a function of the number of relevant input variables. As conjectured in literature this bound is smaller than . This shows that a large number of functions appearing in biological networks belong to a class that has low average sensitivity, which is even close to a tight lower bound. [ABSTRACT FROM AUTHOR]

In this paper the practical density of long‐term DNA storage is increased. Specifically, the DNA weight loading of silica sphere DNA storage is increased to 3.4 wt%, a ten‐fold increase compared to the previous state‐of‐the‐art. By applying a Layer‐by‐Layer (LbL) design with alternating layers of DNA and a polycationic molecule, namely polyethyleneimine (PEI), another dimension to DNA surface binding onto magnetic nanoparticles is added. A protective silica layer is grown on top of the multilayered nanoparticles to shield the DNA from external sources of damage. Accelerated aging experiments of the nanoparticles and the subsequent quantification of DNA stability via qPCR show a significantly lower degradation rate compared to unprotected DNA. The novel material is compared to previous DNA storage technologies, outperforming those in DNA storage density as well as stability. Finally, the storage of an 83 kB digital file in DNA through a successful readout of a 4991 oligonucleotide pool is demonstrated from particle encapsulation, through accelerated aging, to sequencing. [ABSTRACT FROM AUTHOR]

The cover page of the periodical "Angewandte Chemie" for 16 February 2015 issue is presented.

The cover page of the journal "Angewandte Chemie International Edition" is presented.