Ground Truth Signal Research Articles

Optical Flow-Based Extraction of Breathing Signal from Cone Beam CT Projections

Respiratory motion serves as a major challenge during treatment of lung cancer patients using radiotherapy. In this work, an image-based method is presented to extract a respiratory signal directly from Cone Beam CT (CBCT) projections. A dense optical-flow method is used to acquire motion vectors between successive projections in each dataset, followed by the extraction of the dominant motion pattern by application of linear kernel Principal Component Analysis (PCA). The effectiveness of the method was tested on three patient datasets and the extracted breathing signal was compared to a ground-truth signal. The average phase shift was observed to be 1.936 ± 0.734 for patient 1, 1.185 ± 0.781 for patient 2 and 1.537 ± 0.93 for patient 3. Moreover, a 4D CBCT image was reconstructed, considering the respiratory signal extracted, using the proposed method, and compared to that reconstructed considering the ground-truth respiratory signal. Results showed that a minimal difference was found between the image reconstructed using the proposed method and the ground-truth in terms of clarity, motion artifacts and edge sharpness.

Automated classification of cerebral arteries and veins in the neonate using ultrafast doppler spectrogram

Objective.Cerebral arterial and venous flow (A/V) classification is a key parameter for understanding dynamic changes in neonatal brain perfusion. Currently, transfontanellar ultrasound Doppler imaging is the reference clinical technique able to discriminate between A/V using vascular indices such as resistivity index (RI) or pulsatility index (PI). However, under conditions of slow arterial and venular flow, small signal fluctuations can lead to potential misclassifications of vessels. Recently, ultrafast ultrasound imaging has paved the way for better sensitivity and spatial resolution. Here, we show that A/V classification can be performed robustly using ultrafast Doppler spectrogram.Approach.The overall classification steps are as follows: for any pixel within a vessel, a normalized Doppler spectrogram (NDS) is computed that allows for normalized correlation analysis with ground-truth signals that were established semi-automatically based on anatomical/physiological references. Furthermore, A/V classification is performed by computing Pearson correlation coefficient between NDS in ground-truth domains and the individual pixel's NDS inside vessels and finding an optimal threshold.Main Results.When applied to human newborns (n= 40), the overall accuracy, sensitivity, and specificity were found to be 88.5% ± 6.7%, 88.5% ± 6.5%, and 87.0% ± 8.8% respectively. We also examined strategies to fully automate this process, leading to a moderate decrease of 1%-3% in the same metrics. Additionally, when compared to the main clinical metrics such as RI, and PI, the receiver operating characteristic curves exhibited higher areas under the curve; on average by +36% (p< 0.0001) in the full imaging sector, +35% (p= 0.0116) in the cortical regions, +53% (p< 0.0001) in the basal ganglia, +28% (p= 0.0051) in the cingulate gyrus, and +35% (p< 0.0001) in the remaining brain structures.Significance:Our findings suggest that the proposed NDS-based approach can distinguish between A/V when studying cerebral perfusion in neonates.

AnEEG: leveraging deep learning for effective artifact removal in EEG data

In neuroscience and clinical diagnostics, electroencephalography (EEG) is a crucial instrument for capturing neural activity. However, this signal is polluted by different artifacts like muscle activity, eye blinks, environmental interference, etc., which makes it more difficult to retrieve important information from the signal. Deep learning methods have demonstrated the potential to lower these artifacts and enhance the EEG’s quality in recent years. In this work, a novel deep learning method,“AnEEG” is presented for eliminating artifacts from EEG signal. The quantitative matrices NMSE, RMSE, CC, SNR and SAR are calculated to confirm the effectiveness of the proposed model. Through this process, it was found that the suggested model outperformed wavelet decomposition techniques. The model achieves lower NMSE and RMSE values, which indicates better agreement with the original signal. Achieving higher CC values means stronger linear agreement with the ground truth signals. Additionally, the model shows improvements in both SNR and SAR values. Overall, this suggested approach showcases promising results in improving the quality of EEG data by utilizing deep learning.

People make mistakes: Obtaining accurate ground truth from continuous annotations of subjective constructs.

Accurately representing changes in mental states over time is crucial for understanding their complex dynamics. However, there is little methodological research on the validity and reliability of human-produced continuous-time annotation of these states. We present a psychometric perspective on valid and reliable construct assessment, examine the robustness of interval-scale (e.g., values between zero and one) continuous-time annotation, and identify three major threats to validity and reliability in current approaches. We then propose a novel ground truth generation pipeline that combines emerging techniques for improving validity and robustness. We demonstrate its effectiveness in a case study involving crowd-sourced annotation of perceived violence in movies, where our pipeline achieves a .95 Spearman correlation in summarized ratings compared to a .15 baseline. These results suggest that highly accurate ground truth signals can be produced from continuous annotations using additional comparative annotation (e.g., a versus b) to correct structured errors, highlighting the need for a paradigm shift in robust construct measurement over time.

Towards the definition of a standard in TMS-EEG data preprocessing

Combining Non-Invasive Brain Stimulation (NIBS) techniques with the recording of brain electrophysiological activity is an increasingly widespread approach in neuroscience. Particularly successful has been the simultaneous combination of Transcranial Magnetic Stimulation (TMS) and Electroencephalography (EEG). Unfortunately, the strong magnetic pulse required to effectively interact with brain activity inevitably induces artifacts in the concurrent EEG acquisition. Therefore, a careful but aggressive pre-processing is required to efficiently remove artifacts. Unfortunately, as already reported in the literature, different preprocessing approaches can introduce variability in the results. Here we aim at characterizing the three main TMS-EEG preprocessing pipelines currently available, namely ARTIST (Wu et al., 2018), TESA (Rogasch et al., 2017) and SOUND/SSP-SIR (Mutanen et al., 2018, 2016), providing an insight to researchers who need to choose between different approaches. Differently from previous works, we tested the pipelines using a synthetic TMS-EEG signal with a known ground-truth (the artifacts-free to-be-reconstructed signal). In this way, it was possible to assess the reliability of each pipeline precisely and quantitatively, providing a more robust reference for future research. In summary, we found that all pipelines performed well, but with differences in terms of the spatio-temporal precision of the ground-truth reconstruction. Crucially, the three pipelines impacted differently on the inter-trial variability, with ARTIST introducing inter-trial variability not already intrinsic to the ground-truth signal.

Discovering the signal subgraph: An iterative screening approach on graphs

Supervised learning on graphs is a challenging task due to the high dimensionality and inherent structural dependencies in the data, where each edge depends on a pair of vertices. Existing conventional methods are designed for standard Euclidean data and do not account for the structural information inherent in graphs. In this paper, we propose an iterative vertex screening method to achieve dimension reduction across multiple graph datasets with matched vertex sets and associated graph attributes. Our method aims to identify a signal subgraph to provide a more concise representation of the full graphs, potentially benefiting subsequent vertex classification tasks. The method screens the rows and columns of the adjacency matrix concurrently and stops when the resulting distance correlation is maximized. We establish the theoretical foundation of our method by proving that it estimates the true signal subgraph with high probability. Additionally, we establish the convergence rate of classification error under the Erdos-Renyi random graph model and prove that the subsequent classification can be asymptotically optimal, outperforming the entire graph under high-dimensional conditions. Our method is evaluated on various simulated datasets and real-world human and murine graphs derived from functional and structural magnetic resonance images. The results demonstrate its excellent performance in estimating the ground-truth signal subgraph and achieving superior classification accuracy.

Artificial neural network for enhancing signal-to-noise ratio and contrast in photothermal optical coherence tomography

Optical coherence tomography (OCT) is a medical imaging method that generates micron-resolution 3D volumetric images of tissues in-vivo. Photothermal (PT)-OCT is a functional extension of OCT with the potential to provide depth-resolved molecular information complementary to the OCT structural images. PT-OCT typically requires long acquisition times to measure small fluctuations in the OCT phase signal. Here, we use machine learning with a neural network to infer the amplitude of the photothermal phase modulation from a short signal trace, trained in a supervised fashion with the ground truth signal obtained by conventional reconstruction of the PT-OCT signal from a longer acquisition trace. Results from phantom and tissue studies show that the developed network improves signal to noise ratio (SNR) and contrast, enabling PT-OCT imaging with short acquisition times and without any hardware modification to the PT-OCT system. The developed network removes one of the key barriers in translation of PT-OCT (i.e., long acquisition time) to the clinic.

Denoising Seismic Waveforms Using a Wavelet-Transform-Based Machine-Learning Method

ABSTRACT Seismic waveform data recorded at stations can be thought of as a superposition of the signal from a source of interest and noise from other sources. Frequency-based filtering methods for waveform denoising do not result in desired outcomes when the targeted signal and noise occupy similar frequency bands. Recently, denoising techniques based on deep-learning convolutional neural networks (CNNs), in which a recorded waveform is decomposed into signal and noise components, have led to improved results. These CNN methods, which use short-time Fourier transform representations of the time series, provide signal and noise masks for the input waveform. These masks are used to create denoised signal and designaled noise waveforms, respectively. However, advancements in the field of image denoising have shown the benefits of incorporating discrete wavelet transforms (DWTs) into CNN architectures to create multilevel wavelet CNN (MWCNN) models. The MWCNN model preserves the details of the input due to the good time–frequency localization of the DWT. Here, we use a data set of over 382,000 constructed seismograms recorded by the University of Utah Seismograph Stations network to compare the performance of CNN and MWCNN-based denoising models. Evaluation of both models on constructed test data shows that the MWCNN model outperforms the CNN model in the ability to recover the ground-truth signal component in terms of both waveform similarity and preservation of amplitude information. Model evaluation of real-world data shows that both the CNN and MWCNN models outperform standard band-pass filtering (BPF; average improvement in signal-to-noise ratio of 9.6 and 19.7 dB, respectively, with respect to BPF). Evaluation of continuous data suggests the MWCNN denoiser can improve both signal detection capabilities and phase arrival time estimates.

No Head Left Behind – Multi-Head Alignment Distillation for Transformers

Knowledge distillation aims at reducing model size without compromising much performance. Recent work has applied it to large vision-language (VL) Transformers, and has shown that attention maps in the multi-head attention modules of vision-language Transformers contain extensive intra-modal and cross-modal co-reference relations to be distilled. The standard approach is to apply a one-to-one attention map distillation loss, i.e. the Teacher's first attention head instructs the Student's first head, the second teaches the second, and so forth, but this only works when the numbers of attention heads in the Teacher and Student are the same. To remove this constraint, we propose a new Attention Map Alignment Distillation (AMAD) method for Transformers with multi-head attention, which works for a Teacher and a Student with different numbers of attention heads. Specifically, we soft-align different heads in Teacher and Student attention maps using a cosine similarity weighting. The Teacher head contributes more to the Student heads for which it has a higher similarity weight. Each Teacher head contributes to all the Student heads by minimizing the divergence between the attention activation distributions for the soft-aligned heads. No head is left behind. This distillation approach operates like cross-attention. We experiment on distilling VL-T5 and BLIP, and apply AMAD loss on their T5, BERT, and ViT sub-modules. We show, under vision-language setting, that AMAD outperforms conventional distillation methods on VQA-2.0, COCO captioning, and Multi30K translation datasets. We further show that even without VL pre-training, the distilled VL-T5 models outperform corresponding VL pre-trained VL-T5 models that are further fine-tuned by ground-truth signals, and that fine-tuning distillation can also compensate to some degree for the absence of VL pre-training for BLIP models.

Multi-Beam Beamforming-Based ML Algorithm to Optimize the Routing of Drone Swarms

The advancement of wireless networking has significantly enhanced beamforming capabilities in Autonomous Unmanned Aerial Systems (AUAS). This paper presents a simple and efficient classical algorithm to route a collection of AUAS or drone swarms extending our previous work on AUAS. The algorithm is based on the sparse factorization of frequency Vandermonde matrices that correspond to each drone, and its entries are determined through spatiotemporal data of drones in the AUAS. The algorithm relies on multibeam beamforming, making it suitable for large-scale AUAS networking in wireless communications. We show a reduction in the arithmetic and time complexities of the algorithm through theoretical and numerical results. Finally, we also present an ML-based AUAS routing algorithm using the classical AUAS algorithm and feed-forward neural networks. We compare the beamformed signals of the ML-based AUAS routing algorithm with the ground truth signals to minimize the error between them. The numerical error results show that the ML-based AUAS routing algorithm enhances the accuracy of the routing. This error, along with the numerical and theoretical results for over 100 drones, provides the basis for the scalability of the proposed ML-based AUAS algorithms for large-scale deployments.

Single-pulse electrical stimulation artifact removal using the novel matching pursuit-based artifact reconstruction and removal method (MPARRM)

Objective. Single-pulse electrical stimulation (SPES) has been widely used to probe effective connectivity. However, analysis of the neural response is often confounded by stimulation artifacts. We developed a novel matching pursuit-based artifact reconstruction and removal method (MPARRM) capable of removing artifacts from stimulation-artifact-affected electrophysiological signals. Approach. To validate MPARRM across a wide range of potential stimulation artifact types, we performed a bench-top experiment in which we suspended electrodes in a saline solution to generate 110 types of real-world stimulation artifacts. We then added the generated stimulation artifacts to ground truth signals (stereoelectroencephalography signals from nine human subjects recorded during a receptive speech task), applied MPARRM to the combined signal, and compared the resultant denoised signal with the ground truth signal. We further applied MPARRM to artifact-affected neural signals recorded from the hippocampus while performing SPES on the ipsilateral basolateral amygdala in nine human subjects. Main results. MPARRM could remove stimulation artifacts without introducing spectral leakage or temporal spread. It accommodated variable stimulation parameters and recovered the early response to SPES within a wide range of frequency bands. Specifically, in the early response period (5–10 ms following stimulation onset), we found that the broadband gamma power (70–170 Hz) of the denoised signal was highly correlated with the ground truth signal ( R=0.98±0.02 , Pearson), and the broadband gamma activity of the denoised signal faithfully revealed the responses to the auditory stimuli within the ground truth signal with 94%±1.47% sensitivity and 99%±1.01% specificity. We further found that MPARRM could reveal the expected temporal progression of broadband gamma activity along the anterior-posterior axis of the hippocampus in response to the ipsilateral amygdala stimulation. Significance. MPARRM could faithfully remove SPES artifacts without confounding the electrophysiological signal components, especially during the early-response period. This method can facilitate the understanding of the neural response mechanisms of SPES.

A Multi-Level Auto-Adaptive Noise-Filtering Algorithm for Land ICESat-2 Photon-Counting Data

Due to atmospheric scattering, solar radiation, and other factors, the Ice, Cloud, and land Elevation Satellite-2 (ICESat-2) product data suffer from a substantial amount of background noise. This poses a significant challenge when attempting to directly utilize the raw data. Consequently, data denoising becomes an indispensable preprocessing step for its subsequent applications, such as the extraction of forest structure parameters and ground elevation data. While the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm is currently the most widely used method, it remains susceptible to complexities arising from terrain, low signal-to-noise ratio (SNR), and input parameter variations. This paper proposes an efficient Multi-Level Auto-Adaptive Noise Filter (MLANF) algorithm based on photon spatial density. Its purpose is to extract signal photons from ICESat-2 terrestrial data of different ground cover types. The algorithm follows a two-step process. Firstly, random noise photons are removed from the upper and lower regions of the signal photons through a coarse denoising process. Secondly, in the fine denoising step, the K-Nearest Neighbor (KNN) algorithm selects the K photons to calculate the slope along the track. The calculated slope is then used to rotate the direction of the searching neighborhood in the DBSCAN algorithm. The proposed algorithm was tested in eight datasets of four surface types: forest, grassland, desert, and urban, and the extraction results were compared with those from the ATL08 datasets and the DBSCAN algorithm. Based on the ground-truth signal photons obtained by visual inspection, the classification precision, recall, and F-score of our algorithm, as well as two other algorithms, were calculated. The MLANF could achieve a good balance between classification precision (97.48% averaged) and recall (97.96% averaged). Its F-score (97.69% averaged) was higher than that of the other two methods. This demonstrates that the MLANF algorithm successfully obtained a continuous surface profile from ICESat-2 datasets with different surface cover types, significant topographic relief, and low SNR.

Signal domain adaptation network for limited-view optoacoustic tomography

Optoacoustic (OA) imaging is based on optical excitation of biological tissues with nanosecond-duration laser pulses and detection of ultrasound (US) waves generated by thermoelastic expansion following light absorption. The image quality and fidelity of OA images critically depend on the extent of tomographic coverage provided by the US detector arrays. However, full tomographic coverage is not always possible due to experimental constraints. One major challenge concerns an efficient integration between OA and pulse-echo US measurements using the same transducer array. A common approach toward the hybridization consists in using standard linear transducer arrays, which readily results in arc-type artifacts and distorted shapes in OA images due to the limited angular coverage. Deep learning methods have been proposed to mitigate limited-view artifacts in OA reconstructions by mapping artifactual to artifact-free (ground truth) images. However, acquisition of ground truth data with full angular coverage is not always possible, particularly when using handheld probes in a clinical setting. Deep learning methods operating in the image domain are then commonly based on networks trained on simulated data. This approach is yet incapable of transferring the learned features between two domains, which results in poor performance on experimental data. Here, we propose a signal domain adaptation network (SDAN) consisting of i) a domain adaptation network to reduce the domain gap between simulated and experimental signals and ii) a sides prediction network to complement the missing signals in limited-view OA datasets acquired from a human forearm by means of a handheld linear transducer array. The proposed method showed improved performance in reducing limited-view artifacts without the need for ground truth signals from full tomographic acquisitions.

On exact and robust recovery for plug-and-Play compressed sensing

Theoretical understanding of Plug-and-Play (PnP) algorithms, where an off-the-shelf denoiser is used for image regularization, is an active research topic. In this work, we study the problems of exact and stable signal recovery from compressively sensed (CS) measurements using PnP algorithms. We focus on a class of linear denoisers for which it is possible to associate a convex regularizer Φ. We consider the CS problem of minimizing Φ(x) subject to Ax=Aξ, where A is the random sensing matrix and ξ is the ground truth. We prove that if A is Gaussian and ξ lies in the range of the associated denoiser W, then the minimizer is almost surely ξ if rank(W) is less than the number of measurements and almost never otherwise. We extend the result to subgaussian matrices, except that we can guarantee exact recovery only with high probability. For noisy measurements, we consider a robust analogue of the recovery problem and prove that the error between the recovered and the ground-truth signal is bounded by the noise strength. In particular, we derive the sample complexity of CS as a function of reconstruction error and success rate. We perform numerical experiments to validate our theoretical findings.

Deep Constrained Spherical Deconvolution for Robust Harmonization.

Diffusion weighted magnetic resonance imaging (DW-MRI) captures tissue microarchitecture at millimeter scale. With recent advantages in data sharing, large-scale multi-site DW-MRI datasets are being made available for multi-site studies. However, DW-MRI suffers from measurement variability (e.g., inter- and intra-site variability, hardware performance, and sequence design), which consequently yields inferior performance on multi-site and/or longitudinal diffusion studies. In this study, we propose a novel, deep learning-based method to harmonize DW-MRI signals for a more reproducible and robust estimation of microstructure. Our method introduces a data-driven scanner-invariant regularization scheme to model a more robust fiber orientation distribution function (FODF) estimation. We study the Human Connectome Project (HCP) young adults test-retest group as well as the MASiVar dataset (with inter- and intra-site scan/rescan data). The 8th order spherical harmonics coefficients are employed as data representation. The results show that the proposed harmonization approach maintains higher angular correlation coefficients (ACC) with the ground truth signals (0.954 versus 0.942), while achieves higher consistency of FODF signals for intra-scanner data (0.891 versus 0.826), as compared with the baseline supervised deep learning scheme. Furthermore, the proposed data-driven framework is flexible and potentially applicable to a wider range of data harmonization problems in neuroimaging.

Characterizing Infrasound Station Frequency Response Using Large Earthquakes and Colocated Seismometers

ABSTRACT Earthquakes generate infrasound in multiple ways. Acoustic coupling at the surface from vertical seismic velocity, termed local infrasound, is often recorded by infrasound sensors but has seen relatively little study. Over 140 infrasound stations have recently been deployed in Alaska. Most of these stations have single sensors, rather than arrays, and were originally installed as part of the EarthScope Transportable Array. The single sensor nature, paucity of ground-truth signals, and remoteness makes evaluating their data quality and utility challenging. In addition, despite notable recent advances, infrasound calibration and frequency response evaluation remains challenging, particularly for large networks and retrospective analysis of sensors already installed. Here, we examine local seismoacoustic coupling on colocated seismic and infrasound stations in Alaska. Numerous large earthquakes across the region in recent years generated considerable vertical seismic velocity and local infrasound that were recorded on colocated sensors. We build on previous work and evaluate the full infrasound station frequency response using seismoacoustic coupled waves. By employing targeted signal processing techniques, we show that a single seismometer may be sufficient for characterizing the response of an entire nearby infrasound array. We find that good low frequency (&amp;lt;1 Hz) infrasound station response estimates can be derived from large (Mw&amp;gt;7) earthquakes out to at least 1500 km. High infrasound noise levels at some stations and seismic-wave energy focused at low frequencies limit our response estimates. The response of multiple stations in Alaska is found to differ considerably from their metadata and are related to improper installation and erroneous metadata. Our method provides a robust way to remotely examine infrasound station frequency response and examine seismoacoustic coupling, which is being increasingly used in airborne infrasound observations, earthquake magnitude estimation, and other applications.

Heterogeneous separation consistency training for adaptation of unsupervised speech separation

Recently, supervised speech separation has made great progress. However, limited by the nature of supervised training, most existing separation methods require ground-truth sources and are trained on synthetic datasets. This ground-truth reliance is problematic, because the ground-truth signals are usually unavailable in real conditions. Moreover, in many industry scenarios, the real acoustic characteristics deviate far from the ones in simulated datasets. Therefore, the performance usually degrades significantly when applying the supervised speech separation models to real applications. To address these problems, in this study, we propose a novel separation consistency training, termed SCT, to exploit the real-world unlabeled mixtures for improving cross-domain unsupervised speech separation in an iterative manner, by leveraging upon the complementary information obtained from heterogeneous (structurally distinct but behaviorally complementary) models. SCT follows a framework using two heterogeneous neural networks (HNNs) to produce high confidence pseudo labels of unlabeled real speech mixtures. These labels are then updated and used to refine the HNNs to produce more reliable consistent separation results for real mixture pseudo-labeling. To maximally utilize the large complementary information between different separation networks, a cross-knowledge adaptation is further proposed. Together with simulated dataset, those real mixtures with high confidence pseudo labels are then used to update the HNN separation models iteratively. In addition, we find that combing the heterogeneous separation outputs by a simple linear fusion can further slightly improve the final system performance. In this paper, we use cross-dataset to simulate the cross-domain situation in real-life. The term of “source domain” and “target domain” refer to the simulation set for model pre-training and the real unlabeled mixture for model adaptation. The proposed SCT is evaluated on both public reverberant English and anechoic Mandarin cross-domain separation tasks. Results show that, without any available ground-truth of target domain mixtures, the SCT can still significantly outperform our two strong baselines with up to 1.61 dB and 3.44 dB scale-invariant signal-to-noise ratio (SI-SNR) improvements, on the English and Mandarin cross-domain conditions, respectively.

Velocity Estimation of Robot Manipulators: An Experimental Comparison

Accurate velocity information is often essential to the control of robot manipulators, especially for precise tracking of fast trajectories. However, joint velocities are rarely directly measured and instead estimated to save costs. While many approaches have been proposed for the velocity estimation of robot joints, no comprehensive experimental evaluation exists, making it difficult to choose the appropriate method. This paper compares multiple estimation methods running on a six degrees-of-freedom manipulator. We evaluate: 1) the estimation error using a ground-truth signal, 2) the closed-loop tracking error, 3) convergence behavior, 4) sensor fault tolerance, 5) implementation and tuning effort. To ensure a fair comparison, we optimally tune the estimators using a genetic algorithm. All estimation methods have a similar estimation error and similar closed-loop tracking performance, except for the nonlinear high-gain observer, which is not accurate enough. Sliding-mode observers can provide a precise velocity estimation despite sensor faults.

Supervised Learning of Analysis-Sparsity Priors With Automatic Differentiation

Sparsity priors are commonly used in denoising and image reconstruction. For analysis-type priors, a dictionary defines a representation of signals that is likely to be sparse. In most situations, this dictionary is unknown, and is to be recovered from pairs of ground-truth signals and measurements, by minimizing the reconstruction error. This defines a hierarchical optimization problem, which can be cast as a bi-level optimization. Yet, this problem is unsolvable, as reconstructions and their derivative <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">w.r.t.</i> the dictionary have no closed-form expression. However, reconstructions can be iteratively computed using the Forward-Backward splitting (FB) algorithm. In this paper, we approximate reconstructions by the output of the FB algorithm, up to a linear transformation. Then, we leverage automatic differentiation to evaluate the gradient of this output <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">w.r.t.</i> the dictionary, which we learn with projected gradient descent. Experiments show that our algorithm successfully learns the 1D Total Variation (TV) dictionary from piecewise constant signals. For the same case study, we propose to constrain our search to dictionaries of 0-centered columns, which removes undesired local minima and improves numerical stability.

Approximate message passing with spectral initialization for generalized linear models* *This article is an updated version of: Mondelli M and Venkataramanan R 2021 Approximate message passing with spectral initialization for generalized linear models Proc. 24th Int. Conf. Artificial Intelligence and Statistics vol 130, ed A Banerjee and K Fukumizu pp 397–405.

We consider the problem of estimating a signal from measurements obtained via a generalized linear model. We focus on estimators based on approximate message passing (AMP), a family of iterative algorithms with many appealing features: the performance of AMP in the high-dimensional limit can be succinctly characterized under suitable model assumptions; AMP can also be tailored to the empirical distribution of the signal entries, and for a wide class of estimation problems, AMP is conjectured to be optimal among all polynomial-time algorithms. However, a major issue of AMP is that in many models (such as phase retrieval), it requires an initialization correlated with the ground-truth signal and independent from the measurement matrix. Assuming that such an initialization is available is typically not realistic. In this paper, we solve this problem by proposing an AMP algorithm initialized with a spectral estimator. With such an initialization, the standard AMP analysis fails since the spectral estimator depends in a complicated way on the design matrix. Our main contribution is a rigorous characterization of the performance of AMP with spectral initialization in the high-dimensional limit. The key technical idea is to define and analyze a two-phase artificial AMP algorithm that first produces the spectral estimator, and then closely approximates the iterates of the true AMP. We also provide numerical results that demonstrate the validity of the proposed approach.