arXiv subjects

Peter Jung

Publications and source records attributed to Peter Jung.

At least 55 records · Page 3Linked to original sources

arXiv2020

Plug-And-Play Learned Gaussian-mixture Approximate Message Passing

Deep unfolding showed to be a very successful approach for accelerating and tuning classical signal processing algorithms. In this paper, we propose learned Gaussian-mixture AMP (L-GM-AMP) - a plug-and-play compressed sensing (CS) recovery algorithm suitable for any i.i.d. source prior. Our algorithm builds upon Borgerding's learned AMP (LAMP), yet significantly improves it by adopting a universal denoising function within the algorithm. The robust and flexible denoiser is a byproduct of modelling source prior with a Gaussian-mixture (GM), which can well approximate continuous, discrete, as well as mixture distributions. Its parameters are learned using standard backpropagation algorithm. To demonstrate robustness of the proposed algorithm, we conduct Monte-Carlo (MC) simulations for both mixture and discrete distributions. Numerical evaluation shows that the L-GM-AMP algorithm achieves state-of-the-art performance without any knowledge of the source prior.

stat.ML↗

arXiv2020

Laser excited super resolution thermal imaging for nondestructive inspection of internal defects

A photothermal super resolution technique is proposed for an improved inspection of internal defects. To evaluate the potential of the laser-based thermographic technique, an additively manufactured stainless steel specimen with closely spaced internal cavities is used. Four different experimental configurations in transmission, reflection, stepwise and continuous scanning are investigated. The applied image post-processing method is based on compressed sensing and makes use of the block sparsity from multiple measurement events. This concerted approach of experimental measurement strategy and numerical optimization enables the resolution of internal defects and outperforms conventional thermographic inspection techniques.

physics.app-ph↗

arXiv2020

Classification of Spot-welded Joints in Laser Thermography Data using Convolutional Neural Networks

Spot welding is a crucial process step in various industries. However, classification of spot welding quality is still a tedious process due to the complexity and sensitivity of the test material, which drain conventional approaches to its limits. In this paper, we propose an approach for quality inspection of spot weldings using images from laser thermography data.We propose data preparation approaches based on the underlying physics of spot welded joints, heated with pulsed laser thermography by analyzing the intensity over time and derive dedicated data filters to generate training datasets. Subsequently, we utilize convolutional neural networks to classify weld quality and compare the performance of different models against each other. We achieve competitive results in terms of classifying the different welding quality classes compared to traditional approaches, reaching an accuracy of more than 95 percent. Finally, we explore the effect of different augmentation methods.

cs.CV↗

arXiv2020

Robust Instance-Optimal Recovery of Sparse Signals at Unknown Noise Levels

We consider the problem of sparse signal recovery from noisy measurements. Many of frequently used recovery methods rely on some sort of tuning depending on either noise or signal parameters. If no estimates for either of them are available, the noisy recovery problem is significantly harder. The square root LASSO and the least absolute deviation LASSO are known to be noise-blind, in the sense that the tuning parameter can be chosen independent on the noise and the signal. We generalize those recovery methods to the \hrlone{} and give a recovery guarantee once the tuning parameter is above a threshold. Moreover, we analyze the effect of a bad chosen tuning parameter mistuning on a theoretic level and prove the optimality of our recovery guarantee. Further, for Gaussian matrices we give a refined analysis of the threshold of the tuning parameter and proof a new relation of the tuning parameter on the dimensions. Indeed, for a certain amount of measurements the tuning parameter becomes independent on the sparsity. Finally, we verify that the least absolute deviation LASSO can be used with random walk matrices of uniformly at random chosen left regular biparitite graphs.

cs.IT↗

arXiv2020

Efficient Tuning-Free $\ell_1$-Regression of Nonnegative Compressible Signals

In compressed sensing the goal is to recover a signal from as few as possible noisy, linear measurements. The general assumption is that the signal has only a few non-zero entries. The recovery can be performed by multiple different decoders, however most of them rely on some tuning. Given an estimate for the noise level a common convex approach to recover the signal is basis pursuit denoising. If the measurement matrix has the robust null space property with respect to the $\ell_2$-norm, basis pursuit denoising obeys stable and robust recovery guarantees. In the case of unknown noise levels, nonnegative least squares recovers non-negative signals if the measurement matrix fulfills an additional property (sometimes called the $M^+$-criterion). However, if the measurement matrix is the biadjacency matrix of a random left regular bipartite graph it obeys with a high probability the null space property with respect to the $\ell_1$-norm with optimal parameters. Therefore, we discuss non-negative least absolute deviation (NNLAD). For these measurement matrices, we prove a uniform, stable and robust recovery guarantee without the need for tuning. Such guarantees are important, since binary expander matrices are sparse and thus allow for fast sketching and recovery. We will further present a method to solve the NNLAD numerically and show that this is comparable to state of the art methods. Lastly, we explain how the NNLAD can be used for viral detection in the recent COVID-19 crisis.

cs.IT↗

arXiv2020

Neurally Augmented ALISTA

It is well-established that many iterative sparse reconstruction algorithms can be unrolled to yield a learnable neural network for improved empirical performance. A prime example is learned ISTA (LISTA) where weights, step sizes and thresholds are learned from training data. Recently, Analytic LISTA (ALISTA) has been introduced, combining the strong empirical performance of a fully learned approach like LISTA, while retaining theoretical guarantees of classical compressed sensing algorithms and significantly reducing the number of parameters to learn. However, these parameters are trained to work in expectation, often leading to suboptimal reconstruction of individual targets. In this work we therefore introduce Neurally Augmented ALISTA, in which an LSTM network is used to compute step sizes and thresholds individually for each target vector during reconstruction. This adaptive approach is theoretically motivated by revisiting the recovery guarantees of ALISTA. We show that our approach further improves empirical performance in sparse reconstruction, in particular outperforming existing algorithms by an increasing margin as the compression ratio becomes more challenging.

cs.LG↗

arXiv2020

DeepInit Phase Retrieval

This paper shows how data-driven deep generative models can be utilized to solve challenging phase retrieval problems, in which one wants to reconstruct a signal from only few intensity measurements. Classical iterative algorithms are known to work well if initialized close to the optimum but otherwise suffer from non-convexity and often get stuck in local minima. We therefore propose DeepInit Phase Retrieval, which uses regularized gradient descent under a deep generative data prior to compute a trained initialization for a fast classical algorithm (e.g. the randomized Kaczmarz method). We empirically show that our hybrid approach is able to deliver very high reconstruction results at low sampling rates even when there is significant generator model error. Conceptually, learned initializations may therefore help to overcome the non-convexity of the problem by starting classical descent steps closer to the global optimum. Also, our idea demonstrates superior runtime performance over conventional gradient-based reconstruction methods. We evaluate our method for generic measurements and show empirically that it is also applicable to diffraction-type measurement models which are found in terahertz single-pixel phase retrieval.

eess.IV↗

arXiv2020

Sensor Artificial Intelligence and its Application to Space Systems -- A White Paper

Information and communication technologies have accompanied our everyday life for years. A steadily increasing number of computers, cameras, mobile devices, etc. generate more and more data, but at the same time we realize that the data can only partially be analyzed with classical approaches. The research and development of methods based on artificial intelligence (AI) made enormous progress in the area of interpretability of data in recent years. With growing experience, both, the potential and limitations of these new technologies are increasingly better understood. Typically, AI approaches start with the data from which information and directions for action are derived. However, the circumstances under which such data are collected and how they change over time are rarely considered. A closer look at the sensors and their physical properties within AI approaches will lead to more robust and widely applicable algorithms. This holistic approach which considers entire signal chains from the origin to a data product, "Sensor AI", is a highly relevant topic with great potential. It will play a decisive role in autonomous driving as well as in areas of automated production, predictive maintenance or space research. The goal of this white paper is to establish "Sensor AI" as a dedicated research topic. We want to exchange knowledge on the current state-of-the-art on Sensor AI, to identify synergies among research groups and thus boost the collaboration in this key technology for science and industry.

cs.CY↗

arXiv2020

Robust Recovery of Sparse Nonnegative Weights from Mixtures of Positive-Semidefinite Matrices

We consider a structured estimation problem where an observed matrix is assumed to be generated as an $s$-sparse linear combination of $N$ given $n\times n$ positive-semidefinite matrices. Recovering the unknown $N$-dimensional and $s$-sparse weights from noisy observations is an important problem in various fields of signal processing and also a relevant pre-processing step in covariance estimation. We will present related recovery guarantees and focus on the case of nonnegative weights. The problem is formulated as a convex program and can be solved without further tuning. Such robust, non-Bayesian and parameter-free approaches are important for applications where prior distributions and further model parameters are unknown. Motivated by explicit applications in wireless communication, we will consider the particular rank-one case, where the known matrices are outer products of iid. zero-mean subgaussian $n$-dimensional complex vectors. We show that, for given $n$ and $N$, one can recover nonnegative $s$--sparse weights with a parameter-free convex program once $s\leq O(n^2 / \log^2(N/n^2)$. Our error estimate scales linearly in the instantaneous noise power whereby the convex algorithm does not need prior bounds on the noise. Such estimates are important if the magnitude of the additive distortion depends on the unknown itself.

cs.IT↗

arXiv2020

Unsourced Multiuser Sparse Regression Codes achieve the Symmetric MAC Capacity

Unsourced random-access (U-RA) is a type of grant-free random access with a virtually unlimited number of users, of which only a certain number $K_a$ are active on the same time slot. Users employ exactly the same codebook, and the task of the receiver is to decode the list of transmitted messages. Recently a concatenated coding construction for U-RA on the AWGN channel was presented, in which a sparse regression code (SPARC) is used as an inner code to create an effective outer OR-channel. Then an outer code is used to resolve the multiple-access interference in the OR-MAC. In this work we show that this concatenated construction can achieve a vanishing per-user error probability in the limit of large blocklength and a large number of active users at sum-rates up to the symmetric Shannon capacity, i.e. as long as $K_aR < 0.5\log_2(1+K_a\SNR)$. This extends previous point-to-point optimality results about SPARCs to the unsourced multiuser scenario. Additionally, we calculate the algorithmic threshold, that is a bound on the sum-rate up to which the inner decoding can be done reliably with the low-complexity AMP algorithm.

cs.IT↗

arXiv2020

Recovering Structured Data From Superimposed Non-Linear Measurements

This work deals with the problem of distributed data acquisition under non-linear communication constraints. More specifically, we consider a model setup where $M$ distributed nodes take individual measurements of an unknown structured source vector $x_0 \in \mathbb{R}^n$, communicating their readings simultaneously to a central receiver. Since this procedure involves collisions and is usually imperfect, the receiver measures a superposition of non-linearly distorted signals. In a first step, we will show that an $s$-sparse vector $x_0$ can be successfully recovered from $O(s \cdot\log(2n/s))$ of such superimposed measurements, using a traditional Lasso estimator that does not rely on any knowledge about the non-linear corruptions. This direct method however fails to work for several "uncalibrated" system configurations. These blind reconstruction tasks can be easily handled with the $\ell^{1,2}$-Group-Lasso, but coming along with an increased sampling rate of $O(s\cdot \max\{M, \log(2n/s) \})$ observations - in fact, the purpose of this lifting strategy is to extend a certain class of bilinear inverse problems to non-linear acquisition. Our two algorithmic approaches are a special instance of a more abstract framework which includes sub-Gaussian measurement designs as well as general (convex) structural constraints. These results are of independent interest for various recovery and learning tasks, as they apply to arbitrary non-linear observation models. Finally, to illustrate the practical scope of our theoretical findings, an application to wireless sensor networks is discussed, which actually serves as the prototypical example of our methodology.

cs.IT↗

arXiv2019

Sparse Non-Negative Recovery from Biased Subgaussian Measurements using NNLS

We investigate non-negative least squares (NNLS) for the recovery of sparse non-negative vectors from noisy linear and biased measurements. We build upon recent results from [1] showing that for matrices whose row-span intersects the positive orthant, the nullspace property (NSP) implies compressed sensing recovery guarantees for NNLS. Such results are as good as for $\ell_1$-regularized estimators but do not require tuning parameters that depend on the noise level. A bias in the sensing matrix improves this auto-regularization feature of NNLS and the NSP then determines the sparse recovery performance only. We show that NSP holds with high probability for biased subgaussian matrices and its quality is independent of the bias.

cs.IT↗

arXiv2019

Grant-Free Massive Random Access With a Massive MIMO Receiver

We consider the problem of unsourced random access (U-RA), a grant-free uncoordinated form of random access, in a wireless channel with a massive MIMO base station equipped with a large number $M$ of antennas and a large number of wireless single-antenna devices (users). We consider a block fading channel model where the $M$-dimensional channel vector of each user remains constant over a coherence block containing $L$ signal dimensions in time-frequency. In the considered setting, the number of potential users $K_\text{tot}$ is much larger than $L$ but at each time slot only $K_a \ll K_\text{tot}$ of them are active. Previous results, based on compressed sensing, require that $K_a < L$, which is a bottleneck in massive deployment scenarios such as Internet-of-Things and U-RA. In the context of activity detection it is known that such a limitation can be overcome when the number of base station antennas $M$ is sufficiently large and a covariance based recovery algorithm is employed at the receiver. We show that, in the context of U-RA, the same concept allows to achieve high spectral efficiencies in the order of $\mathcal{O}(L \log L)$, although at an exponentially growing complexity. We show also that a concatenated coding scheme can be used to reduce the complexity to an acceptable level while still achieving total spectral efficiencies in the order of $\mathcal{O}(L/\log L)$.

cs.IT↗

arXiv2019

On the Restricted Isometry Property of Centered Self Khatri-Rao Products

In this work we establish the Restricted Isometry Property (RIP) of the centered column-wise self Khatri-Rao (KR) products of $n\times N$ matrix with iid columns drawn either uniformly from a sphere or with iid sub-Gaussian entries. The self KR product is an $n^2\times N$-matrix which contains as columns the vectorized (self) outer products of the columns of the original $n\times N$-matrix. Based on a result of Adamczak et al. we show that such a centered self KR product with independent heavy tailed columns has small RIP constants of order $s$ with probability at least $1-C\exp(-cn)$ provided that $s\lesssim n^2/\log^2(eN/n^2)$. Our result is applicable in various works on covariance matching like in activity detection and MIMO gain-estimation.

cs.IT↗

arXiv2019

Simultaneous structures in convex signal recovery - revisiting the convex combination of norms

In compressed sensing one uses known structures of otherwise unknown signals to recover them from as few linear observations as possible. The structure comes in form of some compressibility including different notions of sparsity and low rankness. In many cases convex relaxations allow to efficiently solve the inverse problems using standard convex solvers at almost-optimal sampling rates. A standard practice to account for multiple simultaneous structures in convex optimization is to add further regularizers or constraints. From the compressed sensing perspective there is then the hope to also improve the sampling rate. Unfortunately, when taking simple combinations of regularizers, this seems not to be automatically the case as it has been shown for several examples in recent works. Here, we give an overview over ideas of combining multiple structures in convex programs by taking weighted sums and weighted maximums. We discuss explicitly cases where optimal weights are used reflecting an optimal tuning of the reconstruction. In particular, we extend known lower bounds on the number of required measurements to the optimally weighted maximum by using geometric arguments. As examples, we discuss simultaneously low rank and sparse matrices and notions of matrix norms (in the "square deal" sense) for regularizing for tensor products. We state an SDP formulation for numerically estimating the statistical dimensions and find a tensor case where the lower bound is roughly met up to a factor of two.

cs.IT↗

arXiv2019

Terahertz dynamic aperture imaging at stand-off distances using a Compressed Sensing protocol

In this text, results of a 0.35 terahertz (THz) dynamic aperture imaging approach are presented. The experiments use an optical modulation approach and a single pixel detector at a stand-off imaging distance of approx 1 meter. The optical modulation creates dynamic apertures of 5cm diameter with approx 2000 individually controllable elements. An optical modulation approach is used here for the first time at a large far-field distance, for the investigation of various test targets in a field-of-view of 8 x 8 cm. The results highlight the versatility of this modulation technique and show that this imaging paradigm is applicable even at large far-field distances. It proves the feasibility of this imaging approach for potential applications like stand-off security imaging or far field THz microscopy.

physics.ins-det↗

arXiv2019

MOCZ for Blind Short-Packet Communication: Some Practical Aspects

We will investigate practical aspects for a recently introduced blind (noncoherent) communication scheme, called modulation on conjugate-reciprocal zeros (MOCZ), which enables reliable transmission of sporadic and short-packets at ultra-low latency in unknown wireless multipath channels, which are static over the receive duration of one packet. Here the information is modulated on the zeros of the transmitted discrete-time baseband signal's $z-$transform. Due to ubiquitous impairments between transmitter and receiver clocks a carrier frequency offset (CFO) will occur after a down-conversion to the baseband, which results in a common rotation of the zeros. To identify fractional rotations of the base angle in the zero-pattern, we propose an oversampled direct zero testing decoder to identify the most likely one. Integer rotations correspond to cyclic shifts of the binary message, which we compensate by a cyclically permutable code (CPC). Additionally, the embedding of CPCs into cyclic codes, allows to exploit additive error correction which reduces the bit-error-rate tremendously. Furthermore, we use the trident structure in the signals autocorrelation to estimate timing offsets and the channels effective delay spread. We finally demonstrate how these impairment estimations can be largely improved by receive antenna diversity, which enables extreme bursty reliable communication at low latency and SNR.

cs.IT↗

arXiv2019

Massive MIMO Unsourced Random Access

We consider an extension of the massive unsourced random access originally proposed by Polyanskiy to the case where the receiver has a very large number of antennas (a massive MIMO base station) and no channel state information is given to the receiver (fully non-coherent detection). Our coding approach borrows the concatenated coding idea from Amalladinne et. al., combined with a novel non-Bayesian `activity detection' algorithm for massive MIMO random access channels, that outperforms currently proposed Bayesian vector AMP (VAMP) schemes currently proposed for activity detection, and does not suffer from the numerical instabilities and requirement for accurate a priori statistics as VAMP. We show that the required transmit $E_b/N_0$ for reliable communication can be made arbitrarily small as the number of receiver antennas M grows sufficiently large.

cs.IT↗