Estimating frequencies of damped sinusoids is the underlying problem of many practical applications. Existing algorithms are often inaccurate for estimating frequencies from damped sinusoids since many of them are designed for undamped signals. In this paper we propose an algorithm to estimate frequencies of a sum of damped sinusoids. This algorithm combines the Gauss-Newton method with an exact formula for single-frequency estimation. As validated by extensive simulations, the proposed algorithm provides nearly optimal estimations of frequencies of damped sinusoids, and is much more efficient than others when the signal has a large number of samples.

Recovering multiband spectra from sub-Nyquist sampling is a prominent research area in signal processing, driven by its wide range of applications and the technical challenges it presents. These challenges demand novel algorithmic approaches tailored to specific scenarios. The problem becomes even more complex when spectral locations are unknown, leading to the development of Blind Multi-Band Sampling techniques. Despite several proposed solutions, a notable research gap persists. Signals with varying energies across different spectral bands often exhibit high-dynamic-range (HDR) features, and with a fixed bit budget, there is a trade-off between optimizing digital resolution and spanning HDR. In this paper, we address this challenge by leveraging the Unlimited Sensing Framework (USF). The interaction between modulo non-linearity and sub-Nyquist sampling induces aliasing in both the domain and range of the signal, further complicating the recovery process, especially with unknown spectral locations. To tackle these challenges, we propose a novel algorithm for blind multiband spectrum recovery from folded samples at sub-Nyquist rates. Importantly, we provide a theoretically guaranteed, perfect recovery at sub-Nyquist sampling rates. Our proof is constructive and leads to an efficient algorithm supported by a novel multi-channel sampling architecture. We validate our approach through numerical experiments, opening up new directions in theory, algorithms, and real-world applications for the field.

The problem of sub-Nyquist multiband sensing has numerous applications across various fields. Despite substantial algorithmic pursuits, the practical implementation of these methods is subject to limitations of digital acquisition via analog-to-digital converters (ADCs). Multiband reconstruction for high-dynamic-range signals that may saturate the ADC is a practical yet challenging problem in many applications. From a different perspective, the Unlimited Sensing Framework (USF) focuses on reconstructing large signals from folded samples yet requires oversampling. The key challenge of multiband reconstruction via sub-Nyquist USF lies in the fundamental stalemate between sub-Nyquist acquisition and the oversampling assumptions required for unfolding. In this paper, we propose a hardware-software co-design approach that enables multiband reconstruction from folded samples at sub-Nyquist rates. The key insight here is to trade the channel redundancy for temporal sampling rate. We extend the multi-coset sampling strategy to the USF context and design a novel reconstruction algorithm. We demonstrate the robustness of our method via Monte-Carlo experiments. Beyond numerical experiments, we build customized hardware and validate our approach through lab experiments. This demonstrates the capabilities of our method in real-world scenarios while creating new avenues and opportunities for the field.

Mainstream signal processing theory and methods are primarily designed for synchronous sampling architectures, where samples are captured at predefined time instants. While this fits well with Shannon’s framework, in the absence of synchronous structure, even fundamental tools like filtering and convolution break down. Alternatively, event-driven or time-encoded sampling offers a more efficient method by capturing signals only when an event occurs. This approach, reminiscent of the "spiking neuron" behavior in the brain, can lead to low-power electronic implementations. Unlike Shannon’s framework, measurements in this scheme are defined by asynchronous sampling, presenting unique challenges. One such open problem is performing spectral estimation from asynchronous samples. In this paper, we propose a novel approach that directly enables spectral estimation from asynchronous measurements. Empirically, our algorithm offers robust, high-resolution spectral information, with a lower sampling rate on trigger times. Beyond numerical experiments, we build an event-driven sampling hardware utilizing asynchronous sigma-delta modulators to validate our approach. These hardware experiments further demonstrate the robustness and practical applicability of our method.

Abstract. In recent years, computational time-of-flight (ToF) imaging has emerged as an exciting and novel imaging modality that offers new and powerful interpretations of natural scenes, with applications extending to three-dimensional, light-in-flight, and non-line-of-sight imaging. Mathematically, ToF imaging relies on algorithmic super-resolution, as the back-scattered sparse light echoes lie on a finer time resolution than what digital devices can capture. Traditional methods necessitate knowledge of the emitted light pulses or kernels and employ sparse deconvolution to recover scenes. Unlike previous approaches, this paper introduces a novel, blind ToF imaging technique that does not require kernel calibration and recovers sparse spikes on a continuum, rather than a discrete grid. By studying the shared characteristics of various ToF modalities, we capitalize on the fact that most physical pulses approximately satisfy the Strang–Fix conditions from approximation theory. This leads to a new mathematical formulation for sparse super-resolution. Our recovery approach uses an optimization method that is pivoted on an alternating minimization strategy. We benchmark our blind ToF method against traditional kernel calibration methods, which serve as the baseline. Extensive hardware experiments across different ToF modalities demonstrate the algorithmic advantages, flexibility, and empirical robustness of our approach. We show that our work facilitates super-resolution in scenarios where distinguishing between closely spaced objects is challenging, while maintaining performance comparable to known kernel situations. Examples of light-in-flight imaging and light-sweep videos highlight the practical benefits of our blind super-resolution method in enhancing the understanding of natural scenes.

The problem of frequency estimation from sub-Nyquist samples has numerous applications across various disciplines and has been extensively studied in signal processing literature. Despite the existence of several algorithmic approaches, the full potential of these methods has not been realized due to the limitations of analog-to-digital converters (ADCs). In particular, accurately estimating frequency for high-dynamic-range signals that may saturate the ADC is still an interesting problem, regardless of the sub-Nyquist aspect. On a different note, the Unlimited Sensing Framework (USF) focuses on recovering large signals from folded samples but requires oversampling. In this paper, we propose a hardware-software co-design approach that allows for frequency estimation from folded samples at sub-Nyquist rates. Our key insight is that temporal redundancy can be eliminated by introducing channel redundancy. Surprisingly, our recovery guarantees are independent of the sampling rate. To achieve this, we introduce a novel multi-channel sampling pipeline coupled with a reconstruction algorithm. Beyond numerical experiments, we build customized hardware and validate our approach through lab experiments. This demonstrates the capabilities of our method in real-world scenarios while opening up new questions for the field.

Recently, contrastive multi-view clustering (MvC) has emerged as a promising avenue for analyzing data from heterogeneous sources, typically leveraging the off-the-shelf instances as positives and randomly sampled ones as negatives. In practice, however, this paradigm would unavoidably suffer from the Dual Noisy Correspondence (DNC) problem, where noise compromises the constructions of both positive and negative pairs. Specifically, the complexity of data collection and transmission might mistake some unassociated pairs as positive (namely, false positive correspondence), while the intrinsic one-to-many contrast nature of contrastive MvC would sample some intra-cluster samples as negative (namely, false negative correspondence). To handle this daunting problem, we propose a novel method, dubbed Contextually-spectral based correspondence refinery (CANDY). CANDY dexterously exploits inter-view similarities as \textit{context} to uncover false negatives. Furthermore, it employs a spectral-based module to denoise correspondence, alleviating the negative influence of false positives. Extensive experiments on five widely-used multi-view benchmarks, in comparison with eight competitive multi-view clustering methods, verify the effectiveness of our method in addressing the DNC problem. The code is available at https://github.com/XLearning-SCU/2024-NeurIPS-CANDY.

Unlimited Sampling Framework (USF) is a digital acquisition protocol that recovers high dynamic range (HDR) input signals from their low dynamic range, modulo samples. Current USF theory and algorithms are predominantly focused on bandlimited signal classes that rely on a relatively high sampling rate. Recently, the "Fourier-Prony" algorithm was proposed and validated via hardware experiments with modulo ADCs. It was shown that this algorithm offers competitive performance in the presence of system noise and quantization, especially when periodic boundary conditions are satisfied.In practice, signals are often measured over a finite observation window and this implies leakage in the Fourier domain. Depending on the severity of spectral leakage, Fourier domain algorithms may fail to reconstruct. To overcome this bottleneck, in this paper, we propose an Iterative Signal Sieving Algorithm (ITER-SIS) that solely operates in the time domain. By utilizing a continuous-domain characterization of modulo samples, ITER-SIS achieves a robust, low-sampling-rate, FFT-free recovery of signals with a finite time observation window, even when there is considerable spectral leakage. Hardware experiments with the modulo ADC demonstrate the robustness of our method in a realistic, noisy and low-sampling rate settings, thus validating its high practical utility in a variety of applications.

To achieve High Dynamic Range (HDR) sensing, the Unlimited Sampling Framework (USF) was recently proposed. In the USF, modulo encoding of the continuous-time input signal prevents the analog-to- digital converter (ADC) from saturation. For recovering the HDR signal from folded samples, reconstruction algorithms are utilized. Current USF pipeline is highly focused on bandlimited signal classes and requires considerable oversampling. In contrast, in this paper, we consider non-bandlimited signals, in particular, sparse inputs with finite-rate-of-innovation (FRI). By devising a novel, dual-channel modulo sampling architecture we show that, surprisingly, sparse signal recovery from modulo samples can be performed independent of the sampling rate. We validate the effectivity of our sampling scheme and show that perfect signal reconstruction is achieved up to machine precision.

While sensors have been widely used in various applications, an essential current trend of research consists of collecting and fusing the information that comes from many sensors. In this paper, on the contrary, we would like to concentrate on a unique mobile sensor; our goal is to unveil the multidimensional information entangled within a stream of one-dimensional data, called FRI Sensing. Our key finding is that, even if we don't have any position knowledge of the moving sensors, it's still possible to reconstruct the sampling trajectory (up to a linear transformation and a shift), and then reconstruct an image that represents the physical sampling field under certain hypotheses. We further investigate the reconstruction hypotheses and propose novel algorithms that could make this 1D to 2D reconstruction feasible. Experiments show that the proposed approach retrieves the sampling image and trajectory accurately under the developed hypotheses. This method can be applied to geolocation localization applications, such as indoor localization and submarine navigation. Moreover, we show that the proposed algorithms have the potential to visualize the one-dimensional signal, which may not be sampled from a real 2D/3D physical field (e.g. speech and text signals), as a two- or three-dimensional image.

Deep learning methods have witnessed the great progress in image restoration with specific metrics (e.g., PSNR, SSIM). However, the perceptual quality of the restored image is relatively subjective, and it is necessary for users to control the reconstruction result according to personal preferences or image characteristics, which cannot be done using existing deterministic networks. This motivates us to exquisitely design a unified interactive framework for general image restoration tasks. Under this framework, users can control continuous transition of different objectives, e.g., the perception-distortion trade-off of image super-resolution, the trade-off between noise reduction and detail preservation. We achieve this goal by controlling the latent features of the designed network. To be specific, our proposed framework, named Controllable Feature Space Network (CFSNet), is entangled by two branches based on different objectives. Our framework can adaptively learn the coupling coefficients of different layers and channels, which provides finer control of the restored image quality. Experiments on several typical image restoration tasks fully validate the effective benefits of the proposed method. Code is available at https://github.com/qibao77/CFSNet.