Kao Kitichotkul

This paper presents an interacting-particle optimization method for composite optimization problems. The proposed approach combines ideas from consensus-based optimization (CBO) with proximal gradient descent. We establish theoretical convergence guarantees for the continuous-time finite-particle dynamics and introduce an alternating update scheme for practical implementation. Finally, we validate the effectiveness of our method across several signal processing problems, demonstrating its advantages over proximal gradient descent, CBO, and their variants.

Equivariant imaging (EI) enables training signal reconstruction models without requiring ground truth data by leveraging signal symmetries. Deep equilibrium models (DEQs) are a powerful class of neural networks where the output is a fixed point of a learned operator. However, training DEQs with complex EI losses requires implicit differentiation through fixed-point computations, whose implementation can be challenging. We show that backpropagation can be implemented modularly, simplifying training. Experiments demonstrate that DEQs trained with implicit differentiation outperform those trained with Jacobian-free backpropagation and other baseline methods. Additionally, we find evidence that EI-trained DEQs approximate the proximal map of an invariant prior.

Single-photon lidar (SPL) measures the time delay between a laser pulse emission and a single photon detection. SPL typically uses a periodic sequence of illumination pulses to improve the accuracy of distance estimates, and the radial velocity of a moving target can also be determined from the Doppler shift in the pulse repetition frequency. Although increasing the repetition frequency increases the photon detection rate, it also decreases the unambiguous range. Several alternative pulsing modes have been proposed to break this tradeoff for SPL measurements of static scenes, e.g., using multiple repetition rates or random pulse trains to yield both high count rates and a long unambiguous range. In this work, we show that velocity can still be estimated despite the use of non-periodic range extension pulse patterns. We derive a general model for the photon acquisition process with a moving target and propose maximum likelihood estimators (MLEs) to recover the distance, velocity, and photon flux levels. Each range extension mode requires a tailored initialization scheme in order for our MLE solver to converge to the global optimum. We demonstrate through simulations and experiments that non-periodic SPL can simultaneously achieve long-range, high-accuracy distance and velocity estimates.

Conventional wisdom suggests that single-photon lidar (SPL) should operate in low-light conditions to minimize dead-time effects. Many methods have been developed to mitigate these effects in synchronous SPL systems. However, solutions for free-running SPL remain limited despite the advantage of reduced histogram distortion from dead times. To improve the accuracy of free-running SPL, we propose a computationally efficient joint maximum likelihood estimator of the signal flux, the background flux, and the depth using only histograms, along with a complementary regularization framework that incorporates a learned point cloud score model as a prior. Simulations and experiments demonstrate that free-running SPL yields lower estimation errors than its synchronous counterpart under identical conditions, with our regularization further improving accuracy.

Readout multiplexing is a promising solution to overcome hardware limitations and data bottlenecks in imaging with single-photon detectors. Conventional multiplexed readout processing creates an upper bound on photon counts at a very fine time scale, where frames with multiple detected photons must either be discarded or allowed to introduce significant bias. We formulate multiphoton coincidence resolution as an inverse imaging problem and introduce a solution framework to probabilistically resolve the spatial locations of photon incidences. Specifically, we develop a theoretical abstraction of row–column multiplexing and a model of photon events that make readouts ambiguous. Using this, we propose a novel estimator that spatially resolves up to four coincident photons. Monte Carlo simulations show that our proposed method increases the peak signal-to-noise ratio (PSNR) of reconstruction by 3 to 4 dB compared to conventional methods under optimal incident flux conditions. Additionally, this method reduces the required number of readout frames to achieve the same mean-squared error as other methods by a factor of 4. Finally, our method matches the Cramer-Rao bound for detection probability estimation for a wider range of incident flux values compared to conventional methods. While demonstrated for a specific detector type and readout architecture, this method can be extended to more general multiplexing with different detector models.

Single-photon lidar (SPL) can accurately measure distances to targets from extremely weak reflections. However, the conventional wisdom holds that pulsed lidar cannot directly measure velocity, unlike other forms of lidar. We present a detection model for SPL that explicitly includes a target’s radial velocity, manifesting as a Doppler shift in the repetition frequency of the received laser pulse train. We propose an approach called Doppler SPL, comprising a pair of methods for jointly estimating range and velocity. Our first method estimates the Doppler shift via Fourier analysis of the detection times. The second method is a maximum likelihood (ML) estimator that can improve the Fourier estimate and enable joint estimation of the flux from signal and background sources. We derive the Cramér–Rao bound for the estimation problem and show via simulations that the ML estimator is statistically efficient across diverse acquisition settings. We also demonstrate simultaneous estimation of range with sub-centimeter accuracy and velocity with 0.1 m/s root mean square error for experimental measurements at 50 frames per second (fps), despite a signal-to-background ratio as low as 0.007. Finally, we present an example of a 3D video reconstruction at 120 fps with per-pixel velocity estimates. With the addition of velocimetry, Doppler SPL has the potential to introduce advanced capabilities in applications such as atmospheric monitoring or autonomous navigation.

The noise in secondary electron (SE) imaging comes from variation in the number of detected SEs and detector imperfections. We recognize that the SE variation itself has two contributors—the source and the sample—that can be separated by closer examination of the signal produced by the detector. Treating SE imaging as a quantitative modality with the goal of pixelwise estimation of SE yield, we use statistically principled techniques to substantially mitigate source noise. We demonstrate a factor of 3 reduction in the required imaging dose. This work opens up broad avenues for quantitative sample mapping at increased speeds and reduced beam currents and characterization of fragile biological samples with electron and ion beams at low- to medium-keV energies. Modern science is dependent on imaging on the nanoscale, often achieved through processes that detect secondary electrons created by a highly focused incident charged particle beam. Multiple types of measurement noise limit the ultimate trade-off between the image quality and the incident particle dose, which can preclude useful imaging of dose-sensitive samples. Existing methods to improve image quality do not fundamentally mitigate the noise sources. Furthermore, barriers to assigning a physically meaningful scale make the images qualitative. Here, we introduce ion count-aided microscopy (ICAM), which is a quantitative imaging technique that uses statistically principled estimation of the secondary electron yield. With a readily implemented change in data collection, ICAM substantially reduces source shot noise. In helium ion microscopy, we demonstrate 3x dose reduction and a good match between these empirical results and theoretical performance predictions. ICAM facilitates imaging of fragile samples and may make imaging with heavier particles more attractive.