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  1. Free, publicly-accessible full text available April 1, 2024
  2. Abstract We consider a regularization problem whose objective function consists of a convex fidelity term and a regularization term determined by the ℓ 1 norm composed with a linear transform. Empirical results show that the regularization with the ℓ 1 norm can promote sparsity of a regularized solution. The goal of this paper is to understand theoretically the effect of the regularization parameter on the sparsity of the regularized solutions. We establish a characterization of the sparsity under the transform matrix of the solution. When the objective function is block-separable or an error bound of the regularized solution to a known function is available, the resulting characterization can be taken as a regularization parameter choice strategy with which the regularization problem has a solution having a sparsity of a certain level. When the objective function is not block-separable, we propose an iterative algorithm which simultaneously determines the regularization parameter and its corresponding solution with a prescribed sparsity level. Moreover, we study choices of the regularization parameter so that the regularization term can alleviate the ill-posedness and promote sparsity of the resulting regularized solution. Numerical experiments demonstrate that the proposed algorithm is effective and efficient, and the choices of the regularization parameters can balance the sparsity of the regularized solution and its approximation to the minimizer of the fidelity function. 
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  3. Abstract

    Frequency modulated continuous wave laser ranging (FMCW LiDAR) enables distance mapping with simultaneous position and velocity information, is immune to stray light, can achieve long range, operate in the eye-safe region of 1550 nm and achieve high sensitivity. Despite its advantages, it is compounded by the simultaneous requirement of both narrow linewidth low noise lasers that can be precisely chirped. While integrated silicon-based lasers, compatible with wafer scale manufacturing in large volumes at low cost, have experienced major advances and are now employed on a commercial scale in data centers, and impressive progress has led to integrated lasers with (ultra) narrow sub-100 Hz-level intrinsic linewidth based on optical feedback from photonic circuits, these lasers presently lack fast nonthermal tuning, i.e. frequency agility as required for coherent ranging. Here, we demonstrate a hybrid photonic integrated laser that exhibits very narrow intrinsic linewidth of 25 Hz while offering linear, hysteresis-free, and mode-hop-free-tuning beyond 1 GHz with up to megahertz actuation bandwidth constituting 1.6 × 1015Hz/s tuning speed. Our approach uses foundry-based technologies - ultralow-loss (1 dB/m) Si3N4photonic microresonators, combined with aluminium nitride (AlN) or lead zirconium titanate (PZT) microelectromechanical systems (MEMS) based stress-optic actuation. Electrically driven low-phase-noise lasing is attained by self-injection locking of an Indium Phosphide (InP) laser chip and only limited by fundamental thermo-refractive noise at mid-range offsets. By utilizing difference-drive and apodization of the photonic chip to suppress mechanical vibrations of the chip, a flat actuation response up to 10 MHz is achieved. We leverage this capability to demonstrate a compact coherent LiDAR engine that can generate up to 800 kHz FMCW triangular optical chirp signals, requiring neither any active linearization nor predistortion compensation, and perform a 10 m optical ranging experiment, with a resolution of 12.5 cm. Our results constitute a photonic integrated laser system for scenarios where high compactness, fast frequency actuation, and high spectral purity are required.

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  4. Recent advancements in semiconductor technologies have stimulated the growth of ultra-low power wearable devices. However, these devices often pose critical constraints in usability and functionality because of the on-device battery as the primary power source [1]. For example, periodic charging of wearable devices hampers the continuous monitoring of users' fitness or health conditions [2], and batteries and charging equipment have been identified as one of the most rapidly growing electronic waste streams [3]. To counteract the above-mentioned complications associated with the management of on-device batteries, wireless power transmission technologies capable of charging wearable devices in a completely unobtrusive and seamless manner have become an emerging topic of research over the past decade [4]. Researchers have instrumented daily objects or the surrounding environment with equipment that can wirelessly transfer energy from a variety of sources, such as Radio Frequency (RF) signals, laser, and electromagnetic fields [5]. However, these solutions require large and costly infrastructure and/or need to transmit a significant amount of power to support reasonable power harvesting at the wearable devices, which conflict with the vision of ubiquitously available and scalable charging support. 
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  5. This work proposes a robotic pipeline for picking and constrained placement of objects without geometric shape priors. Compared to recent efforts developed for similar tasks, where every object was assumed to be novel, the proposed system recognizes previously manipulated objects and performs online model reconstruction and reuse. Over a lifelong manipulation process, the system keeps learning features of objects it has interacted with and updates their reconstructed models. Whenever an instance of a previously manipulated object reappears, the system aims to first recognize it and then register its previously reconstructed model given the current observation. This step greatly reduces object shape uncertainty allowing the system to even reason for parts of objects, which are currently not observable. This also results in better manipulation efficiency as it reduces the need for active perception of the target object during manipulation. To get a reusable reconstructed model, the proposed pipeline adopts: i) TSDF for object representation, and ii) a variant of the standard particle filter algorithm for pose estimation and tracking of the partial object model. Furthermore, an effective way to construct and maintain a dataset of manipulated objects is presented. A sequence of real-world manipulation experiments is performed. They show how future manipulation tasks become more effective and efficient by reusing reconstructed models of previously manipulated objects, which were generated during their prior manipulation, instead of treating objects as novel every time. 
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  6. In this article, we introduce a compact representation for measured BRDFs by leveraging Neural Processes (NPs). Unlike prior methods that express those BRDFs as discrete high-dimensional matrices or tensors, our technique considers measured BRDFs as continuous functions and works in corresponding function spaces . Specifically, provided the evaluations of a set of BRDFs, such as ones in MERL and EPFL datasets, our method learns a low-dimensional latent space as well as a few neural networks to encode and decode these measured BRDFs or new BRDFs into and from this space in a non-linear fashion. Leveraging this latent space and the flexibility offered by the NPs formulation, our encoded BRDFs are highly compact and offer a level of accuracy better than prior methods. We demonstrate the practical usefulness of our approach via two important applications, BRDF compression and editing. Additionally, we design two alternative post-trained decoders to, respectively, achieve better compression ratio for individual BRDFs and enable importance sampling of BRDFs. 
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