Integrate-and-fire time-encoding machines (IF-TEMs) are an alternative to conventional uniform sampling, where the signals are measured based on their variations. While IF-TEMs excel in energy efficiency through their event-driven sampling approach, they often oversample significantly to ensure accurate signal reconstruction. The adaptive IF-TEM method proposed in the literature addresses oversampling but lacks theoretical guarantees. In this work, we proposed a variable-bias IF-TEM that uses signals’ bandwidth and energy to reduce oversampling. We derived theoretical guarantees and ensured that the method always results in perfect reconstruction while reducing oversampling. We presented simulation results to support the claims and show that the proposed method results in lower error and fewer samples than the existing techniques.

Modulo-folding ADCs (MF-ADCs) offer a potential alternative to conventional ADCs by requiring fewer bits. However, the algorithms that follow an MF-ADC typically require an unfolding method, which demands significant oversampling. In this paper, we explore the problem of symbol detection in digital communication at a receiver using an MF-ADC. We demonstrate that, in certain noisy conditions, unfolding is not necessary for detection, allowing the MF-ADC to operate at a lower rate. Additionally, we show that any unfolding process may negate the benefits of fewer bits or reduced quantization error associated with MF-ADCs. We derive theoretical bounds and discuss optimal symbol design to achieve the best performance. The proposed approach, which eliminates the need for unfolding, can facilitate the development of low-rate MF-ADCs for various other applications.

The challenge of sensor selection involves choosing a subset of the available measurements to estimate data while aiming to minimize estimation errors. Traditionally, convex relaxation methods with solvers like the projected subgradient (PSG) algorithm have been employed to address this problem. However, they are computationally intensive due to the large number of iterations involved and necessitate accurate apriori knowledge of the noise statistics, which may be unavailable. Moreover, in the case of linear measurements, the cost functions involved are data-independent, which makes them non-adaptive. In this paper, we tackle these challenges by introducing two deep neural networks that unfold the PSG algorithm. These networks are trained on observations where knowledge of noise statistics and the parameters to estimate are implicit. This makes the approach data-adaptive without needing any priors. Moreover, in comparison to the conventional PSG algorithm, the unfoldings require fewer iterations. Experimental results demonstrate that these networks achieve a lower mean-squared error by 4 10 dB compared to the standard PSG algorithm or random selection.

Compressive sensing (CS) techniques for estimating the direction-of-arrival (DoA) stand apart from traditional approaches due to their ability to derive DoA information from just a single snapshot, eliminating the need for a large number of snapshots. This research addresses the challenge of adaptively choosing sensors for each snapshot during DoA tracking. We have devised a greedy algorithm for sensor selection, incorporating a submodular cost function based on our proposed deterministic prior models for DoA. Notably, we show that this selection algorithm is equally efficient compared to the conventional greedy method that relies on exact knowledge of the DOAs. We also introduce a modified version of a conventional CS-reconstruction algorithm that takes advantage of prior information to reduce the required number of measurements and computational time. We demonstrate that the tracking accuracy is improved when using the deterministic priors for sensor selection and subsequent reconstruction.

In this study, we consider a variant of unlabelled sensing where the measurements are sparsely permuted, and additionally, a few correspondences are known. We present an estimator to solve for the unknown vector. We derive a theoretical upper bound on the ℓ2reconstruction error of the unknown vector. Through numerical experiments, we demonstrate that the additional known correspondences result in a significant improvement in the reconstruction error. Additionally, we compare our estimator with the classical robust regression estimator and we find that our method outperforms it on the normalized reconstruction error metric by up to 20% in the high permutation regimes (> 30%). Lastly, we showcase the practical utility of our framework on a non-rigid motion estimation problem. We show that using a few manually annotated points along point pairs with the key-point (SIFT-based) descriptor pairs with unknown or incorrectly known correspondences can improve motion estimation.

Vintage videos, as well as modern day videos acquired at high frame rates, suffer from a visually disturbing artifact called flicker, which is the rapid change in average intensity across consecutive frames. Vintage videos also suffer from blotch artifacts, i.e., each video frame contains small regions at random locations with undefined pixel values. We present a model-based learning approach to remove flicker as well as blotches simultaneously. Our work uses a pixel-wise affine intensity model for flicker between neighboring frames, with coefficients that vary smoothly in the spatial sense but randomly across time. Due to smooth spatial variation, the flicker coefficients for any given frame can be modelled as linear combinations of low-frequency discrete cosine transform (DCT) bases. We also model blotches as heavy-tailed but sparse artifacts affecting every frame. We then present a novel framework to restore the video frames by jointly estimating the blotches as well as the DCT coefficients of the flicker via convex optimization. Given the high computational cost of the optimization-based method for processing an entire video, we use a deep unrolled neural network approach to achieve similar restoration quality at significantly reduced cost. Our approach is completely unsupervised and model-based, and hence simple and interpretable. It produces high-quality reconstructions, in terms of visual appeal as well as numerical metrics, on a variety of vintage videos as well as high-speed videos. It does not suffer from generalization issues unlike some recent state-of-the-art supervised methods which use end-to-end neural networks for restoration.

In the problem of sensor selection, observations from L out of N sensors are chosen for data estimation, with the objective of minimizing an error metric. It is well known that a greedy selection (GS) method can achieve an error metric which is not worse than 1/e from that of the optimal algorithm, for a wide class of sensor selection problems. However, GS does not scale well with the problem size. The available accelerators to GS also fail to solve large scale problems in any reasonable time. In this paper, we propose a clustering-based solution called clustered greedy selection (CGS) which not only reduces the problem size, but also achieves a similar performance to GS. CGS first clusters the sensors based on a similarity metric and then applies GS on this lower dimensional problem. The method seems particularly suitable when the number of sensors to be selected is much less than the total number of sensors. We provide bounds for the worst-case performance of CGS and experimentally validate our results on some linear models.

Modulo folding can be used to sample high-dynamic range signals without increasing the dynamic range of the sampler. Specifically, folding is used prior to sampling and then the folded signal is sampled. After sampling, unfolding algorithms are used to compute the true samples (up to a constant factor) from the folded ones. In this work, we consider a modulo sampling framework for finite rate of innovation (FRI) signals which are used to model signals in time of flight imaging. We suggest compactly supported sum-of-sincs filter as a sampling kernel prior to modulo folding and sampling. We derive conditions on the sampling rate and filter coefficients which lead to unfolding of the samples up to an unknown constant. We then propose a modified annihilating filter approach that can uniquely determine the FRI parameters from the unfolded samples with a constant unknown offset. We show that the proposed framework outperforms existing techniques in the presence of noise.

In practice, Analog-to-Digital Converter (ADC) is used to perform sampling. A practical bottleneck of ADC is its lower dynamic range, leading to loss of information. To address this issue, researchers suggested folding operation on the signal using a modulo operator before passing it as an input to ADC. Though this process preserves the signal information, an unfolding algorithm is required to get the true samples from the folded samples. Noise robustness and computational time are two key parameters of an unfolding algorithm. In this paper, we propose a fast and robust algorithm for unfolding. Specifically, we first show that the first-order difference of the residual samples (the difference between the folded and true samples) is sparse by deriving an upper bound on its sparsity, and can be recovered from its partial Fourier measurements by formulating a sparse recovery problem. We demonstrate that the proposed algorithm is robust to noise and computationally efficient compared to the existing methods.

Recovering multiple measurement vectors (MMVs) with common sparse support from compressed measurements is an important problem in many applications. Theoretical results and practical algorithms that use rank properties of the MMVs have been shown to require fewer measurements. These methods use the same number of measurements for all vectors or channels, which may not be efficient. The rank-aware algorithms fail in the presence of noise as the rank property is lost. We propose an alternative strategy in which only a few channels are used for support recovery. These channels require larger measurements compared to the rest but lead to a reduction in the total number of measurements. We propose a robust rank-aware algorithm to tackle noisy scenarios and show that it results in lower errors in the estimation of sparse vectors compared to the existing approaches. The algorithm also allows trade off between the measurements and channels, which helps design flexible systems.

Two important attributes of analog to digital converters (ADCs) are its sampling rate and dynamic range. The sampling rate should be greater than or equal to the Nyquist rate for bandlimited signals with bounded energy. It is also desired that the signals’ dynamic range should be within that of the ADC’s; otherwise, the signal will be clipped. A modulo operator has been recently suggested prior to sampling to restrict the dynamic range. Due to the nonlinearity of the modulo operation, the samples are distorted. Existing recovery algorithms to recover the signal from its modulo samples operate at a high sampling rate and are not robust in the presence of noise. In this paper, we propose a robust algorithm to recover the signal from the modulo samples which operates at lower sampling rate compared to existing techniques. We also show that our method has lower error compared to existing approaches for a given sampling rate, noise level, and dynamic range of the ADC. Our results lead to less constrained hardware design to address dynamic range issues while operating at the lowest rate possible.

Finite-rate-of-innovation (FRI) signals are ubiquitous in radar, ultrasound, and time of flight imaging applications. In this paper, we propose a model-based deep learning approach to jointly design the subsampling and reconstruction of FRI signals. Specifically, our framework is a combination of a greedy subsampling algorithm and a learning-based sparse recovery method. Unlike existing learning-based techniques, the proposed algorithm can flexibly handle changes in the sampling rate and does not suffer from differentiability issues during training. Moreover, exact knowledge of the FRI pulse is not required. Numerical results show that the proposed joint design leads to lower reconstruction error for FRI signals compared with existing benchmark methods for a given number of samples. The method can easily adapt to other sparse recovery problems.

In this paper, we study the problem of sampling finite-rate-of-innovation (FRI) signals by using an integrate-and-fire time encoding machine. We consider a Fourier-domain reconstruction approach and design a robust sampling kernel that has a frequency-domain alias cancellation condition and excludes the zero frequency. In the absence of noise, we present theoretical recovery guarantees for FRI signals with arbitrary pulse shapes using our approach. We show that the minimum firing rate is proportional to the rate of innovation of the FRI signal. In the presence of noise, our technique results in 2−10 dB lower error while estimating the FRI parameters compared to existing methods for the same number of measurements.

Sub-Nyquist sampling is used in modern high-resolution pulse-Doppler radar systems to reduce system resources and improve resolution. Xampling with Doppler focusing is utilized to implement these sub-Nyquist radar systems. Signal recovery involves iterative optimization requiring large computational time that may be prohibitive in real applications. In this paper, we propose Deep Unfolded Radar Sensing (DURAS), a model-based deep learning architecture to address this problem. We utilize the recently introduced complex LISTA (C-LISTA) with recurrent neural network units and complex soft-thresholding to handle the complex-valued measurement signals. We propose a partial Doppler focusing (PDF) framework with ensembling of multiple PDF measurement vectors via a convolutional neural network (CNN). This CNN followed by a complex cardioid activation function is added to the front end of the C-LISTA architecture. Thus, DURAS is a hybrid architecture of partial Doppler focusing, CNN, and C-LISTA that provides considerably improved performance compared to existing methods on target detection in radar systems.

We consider a continuous-time sparse multichannel blind deconvolution problem. The signal at each channel is expressed as the convolution of a common source signal and its impulse response given as a sparse filter. The objective is to identify these sparse filters from sub-Nyquist samples of channel outputs by leveraging the correlation across channels. We present necessary and sufficient conditions for the unique identification. In particular, the sparse filters should not share a common sparse convolution factor and it is necessary to have 2L or more samples per channel from at least two distinct channels. We also show that L-sparse filters are uniquely identifiable from two channels provided that there are 2L2Fourier measurements per channel, which can be computed from sub-Nyquist samples. Additionally, in the asymptotic of the number of channels, 2L Fourier measurements per channel are sufficient. The results are applicable to the design of multi-receiver, low-rate, sensors in applications such as radar, sonar, ultrasound, and seismic exploration.

We propose a learned-structured unfolding neural network for the problem of compressive sparse multichannel blind-deconvolution. In this problem, each channel’s measurements are given as convolution of a common source signal and sparse filter. Unlike prior works where the compression is achieved either through random projections or by applying a fixed structured compression matrix, this paper proposes to learn the compression matrix from data. Given the full measurements, the proposed network is trained in an unsupervised fashion to learn the source and estimate sparse filters. Then, given the estimated source, we learn a structured compression operator while optimizing for signal reconstruction and sparse filter recovery. The efficient structure of the compression allows its practical hardware implementation. The proposed neural network is an autoencoder constructed based on an unfolding approach: upon training, the encoder maps the compressed measurements into an estimate of sparse filters using the compression operator and the source, and the linear convolutional decoder reconstructs the full measurements. We demonstrate that our method is superior to classical structured compressive sparse multichannel blind-deconvolution methods in terms of accuracy and speed of sparse filter recovery.

Standard approaches for ellipse fitting are based on the minimization of algebraic or geometric distance between the given data and a template ellipse. When the data are noisy and come from a partial ellipse, the state-of-the-art methods tend to produce biased ellipses. We rely on the sampling structure of the underlying signal and show that the x - and y -coordinate functions of an ellipse are finite-rate-of-innovation (FRI) signals, and that their parameters are estimable from partial data. We consider both uniform and nonuniform sampling scenarios in the presence of noise and show that the data can be modeled as a sum of random amplitude-modulated complex exponentials. A low-pass filter is used to suppress noise and approximate the data as a sum of weighted complex exponentials. The annihilating filter used in FRI approaches is applied to estimate the sampling interval in the closed form. We perform experiments on simulated and real data, and assess both objective and subjective performances in comparison with the state-of-the-art ellipse fitting methods. The proposed method produces ellipses with lesser bias. Furthermore, the mean-squared error is lesser by about 2 to 10 dB. We show the applications of ellipse fitting in iris images starting from partial edge contours, and to free-hand ellipses drawn on a touch-screen tablet.

A typical finite-rate-of-innovation (FRI) signal reconstruction scheme is based on the measurement of uniform samples in time/frequency domain, and the application of the annihilating filter on the measured samples. We propose a continuous-time annihilation framework for a class of FRI signals. In particular, we show that FRI signals of sum-of-weighted exponential form can be annihilated by a composition of translation operators and show that the parameters of the signal can be estimated in the periodic non-uniform sampling (PNU) scenario. We discuss the advantages of PNU sampling over uniform sampling and extend it for general FRI signal sampling and reconstruction. Simulations are performed and the results are compared with state-of-the-art methods for signal-to-noise ratios ranging from -20 to 100 dB. An improvement in the estimation accuracy of 15-55 dB in terms of bias and mean-square error is achieved over conventional methods by a rearrangement of uniform samples to follow PNU sampling.

We address the problem of parameter estimation of an ellipse from a limited number of samples. We develop a new approach for solving the ellipse fitting problem by showing that the x and y coordinate functions of an ellipse are finite-rate-of-innovation (FRI) signals. Uniform samples of x and y coordinate functions of the ellipse are modeled as a sum of weighted complex exponentials, for which we propose an efficient annihilating filter technique to estimate the ellipse parameters from the samples. The FRI framework allows for estimating the ellipse parameters reliably from partial or incomplete measurements even in the presence of noise. The efficiency and robustness of the proposed method is compared with state-of-art direct method. The experimental results show that the estimated parameters have lesser bias compared with the direct method and the estimation error is reduced by 5-10 dB relative to the direct method.

We consider the problem of parameter estimation from real-valued multi-tone signals. Such problems arise frequently in spectral estimation. More recently, they have gained new importance in finite-rate-of-innovation signal sampling and reconstruction. The annihilating filter is a key tool for parameter estimation in these problems. The standard annihilating filter design has to be modified to result in accurate estimation when dealing with real sinusoids, particularly because the real-valued nature of the sinusoids must be factored into the annihilating filter design. We show that the constraint on the annihilating filter can be relaxed by making use of the Hilbert transform. We refer to this approach as the Hilbert annihilating filter approach. We show that accurate parameter estimation is possible by this approach. In the single-tone case, the mean-square error performance increases by 6 dB for signal-to-noise ratio (SNR) greater than 0 dB. We also present experimental results in the multi-tone case, which show that a significant improvement (about 6dB) is obtained when the parameters are close to 0 or π. In the mid-frequency range, the improvement is about 2 to 3dB.

Recently, a method of finding the spectral samples of non-periodic-finite-rate-of-innovation (NP-FRI) signals using a sum-of-sincs (SoS) sampling kernel was proposed in the literature. In the SoS approach, the kernel is repeated at a rate dependent on the delays of the FRI signal. The number of repetitions depends on both the duration and the delays of pulses constituting the FRI signal. In this paper, we show that the kernel repetition can be avoided and perfect reconstruction can be obtained by working with the SoS kernel directly provided that certain sampling criteria are satisfied. We place a lower bound on the sampling rate to ensure that exact signal reconstruction is achieved using filtered samples. To suppress the effect of noise, we use Cadzow denoising technique. Reconstruction is achieved using the annihilating filter method. We report results on data simulated using Field II software as well as real cardiac ultrasound data. The experimental results show that, with nearly 10 times less data than that required by the standard technique, the proposed method gives a comparable quality of reconstruction. The reconstruction accuracy can be controlled by choosing the model order of the NP-FRI signal appropriately.