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Characterization of point-source transient events with a rolling-shutter compressed sensing system

Frank Qiu, Joshua Michalenko, Lilian K. Casias, Cameron J. Radosevich, Jon Slater, Eric A. Shields

TL;DR

This work tackles the problem of detecting and characterizing extremely fast and small optical events (PSTEs) by marrying rolling-shutter imaging with compressed sensing. The authors introduce a differences-based CS objective solved via Fast Iterative Shrinkage-Thresholding Algorithm (FISTA), including a blocked version that enhances speed and reduces error accumulation. Theoretical guarantees based on RIP are developed for the rolling-shutter sensing process, providing bounds on reconstruction error in terms of sparsity, block structure, and noise. Through simulations, the proposed Blocked FISTA-D algorithm outperforms TV and standard $\ell^1$ approaches in both speed and reconstruction quality, and hardware considerations (double shutter, faster cameras) are proposed to mitigate spatial-coverage artifacts, illustrating a path toward faster, cheaper PSTE sensing systems.

Abstract

Point-source transient events (PSTEs) - optical events that are both extremely fast and extremely small - pose several challenges to an imaging system. Due to their speed, accurately characterizing such events often requires detectors with very high frame rates. Due to their size, accurately detecting such events requires maintaining coverage over an extended field-of-view, often through the use of imaging focal plane arrays (FPA) with a global shutter readout. Traditional imaging systems that meet these requirements are costly in terms of price, size, weight, power consumption, and data bandwidth, and there is a need for cheaper solutions with adequate temporal and spatial coverage. To address these issues, we develop a novel compressed sensing algorithm adapted to the rolling shutter readout of an imaging system. This approach enables reconstruction of a PSTE signature at the sampling rate of the rolling shutter, offering a 1-2 order of magnitude temporal speedup and a proportional reduction in data bandwidth. We present empirical results demonstrating accurate recovery of PSTEs using measurements that are spatially undersampled by a factor of 25, and our simulations show that, relative to other compressed sensing algorithms, our algorithm is both faster and yields higher quality reconstructions. We also present theoretical results characterizing our algorithm and corroborating simulations. The potential impact of our work includes the development of much faster, cheaper sensor solutions for PSTE detection and characterization.

Characterization of point-source transient events with a rolling-shutter compressed sensing system

TL;DR

This work tackles the problem of detecting and characterizing extremely fast and small optical events (PSTEs) by marrying rolling-shutter imaging with compressed sensing. The authors introduce a differences-based CS objective solved via Fast Iterative Shrinkage-Thresholding Algorithm (FISTA), including a blocked version that enhances speed and reduces error accumulation. Theoretical guarantees based on RIP are developed for the rolling-shutter sensing process, providing bounds on reconstruction error in terms of sparsity, block structure, and noise. Through simulations, the proposed Blocked FISTA-D algorithm outperforms TV and standard approaches in both speed and reconstruction quality, and hardware considerations (double shutter, faster cameras) are proposed to mitigate spatial-coverage artifacts, illustrating a path toward faster, cheaper PSTE sensing systems.

Abstract

Point-source transient events (PSTEs) - optical events that are both extremely fast and extremely small - pose several challenges to an imaging system. Due to their speed, accurately characterizing such events often requires detectors with very high frame rates. Due to their size, accurately detecting such events requires maintaining coverage over an extended field-of-view, often through the use of imaging focal plane arrays (FPA) with a global shutter readout. Traditional imaging systems that meet these requirements are costly in terms of price, size, weight, power consumption, and data bandwidth, and there is a need for cheaper solutions with adequate temporal and spatial coverage. To address these issues, we develop a novel compressed sensing algorithm adapted to the rolling shutter readout of an imaging system. This approach enables reconstruction of a PSTE signature at the sampling rate of the rolling shutter, offering a 1-2 order of magnitude temporal speedup and a proportional reduction in data bandwidth. We present empirical results demonstrating accurate recovery of PSTEs using measurements that are spatially undersampled by a factor of 25, and our simulations show that, relative to other compressed sensing algorithms, our algorithm is both faster and yields higher quality reconstructions. We also present theoretical results characterizing our algorithm and corroborating simulations. The potential impact of our work includes the development of much faster, cheaper sensor solutions for PSTE detection and characterization.
Paper Structure (25 sections, 3 theorems, 43 equations, 11 figures, 2 algorithms)

This paper contains 25 sections, 3 theorems, 43 equations, 11 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Imaging System Overview
  3. Algorithms Overview
  4. Algorithm \ref{['alg:FISTA_Diff']}: FISTA with Differences
  5. Algorithm \ref{['alg:BlockedFISTA-D']}: Blocked FISTA with Differences
  6. Theoretical Characterization
  7. Rolling Shutter and the Restricted Isometry Property
  8. Reconstruction Error Bounds
  9. Simulation Results
  10. Comparison to Alternative Reconstruction Algorithms
  11. Validation of Theorem \ref{['thm:avgErrDiff']} in Simulation
  12. Reconstruction up to the Nyquist Limit
  13. Practical Considerations
  14. An Explanation of the Artifact
  15. Increasing Spatial Coverage through a Double Shutter System
  16. ...and 10 more sections

Key Result

Theorem 4.1

Let $\zeta \in \mathbb{R}^n$ be a random vector with independent, mean-zero, variance one, $S$-subgaussian entries. Let $A \in \mathbb{R}^{m \times n}$ be the matrix defined as $Ax \equiv \frac{1}{\sqrt{m}} P_m [\zeta \ast x]$ for some projection matrix $P_m: \mathbb{R}^n \rightarrow \mathbb{R}^m$. then with probability at least $1 - \eta$, the restricted isometry constant of the matrix $A$ satis

Figures (11)

  • Figure 1: Overview of the simulated rolling shutter system in Sections \ref{['sec:Experiments']} and \ref{['sec:PractConsid']}. On the left is the diffuser's PSF, recorded from a physical phase diffuser VidFromStills. On the right, we visualize the sampling schedule of the rolling shutter over time, with the white lines representing the sampled lines. Note that the diffuser's PSF spreads a signal over most of the FPA, which combats the spatial undersampling inherent to the rolling shutter readout.
  • Figure 2: Visualization of the various stages of processing in our rolling shutter imaging system. The top row shows the raw input signal of a light source moving horizontally. The middle row shows the result of passing the input through the phase diffuser. The bottom row shows measurements recorded from the rolling shutter readout. From these measurements, we recover the original signal of the top row by applying our reconstruction algorithms in Section \ref{['sec:AlgoOverview']}.
  • Figure 3: FISTA with Differences (FISTA-D)
  • Figure 4: On the left is a 1D signal consisting of four sequential pulses of roughly $15Hz$, $50Hz$, $100Hz$, and $400Hz$, with a duration of $300ms$. The PSTE was generated by multiplying this 1D signal with a $128 \times 128$ Gaussian, shown on the right, to generate a $128 \times 128 \times 300$ movie. Spatially, the PSTE is roughly 3 pixels in diameter. Our simulated rolling shutter reads 5 lines per sample at $1000Hz$, corresponding to a global shutter rate of roughly $40Hz$.
  • Figure 5: Comparison of three compressed sensing algorithms: blocked differences ($B = 50$), a TV variant, and a standard $\ell^1$ variant. We plot the center pixel intensity of each reconstruction, where the PSTE is spatially localized. The two alternative algorithms suffer from a dropout artifact which is not noticeably present in our algorithm. Our algorithm ($31.1s$) was significantly faster than both the $\ell^1$ algorithm ($64.4s$) and TV algorithm ($190.8s$).
  • ...and 6 more figures

Theorems & Definitions (5)

  • Theorem 4.1: Theorem 4.1 krahmer2013suprema
  • Theorem 4.2
  • Lemma B.1
  • proof
  • proof