Closed-form inverses for the mixed pixel/multipath interference problem in AMCW lidar

We present two new closed-form methods for mixed pixel/multipath interference separation in AMCW lidar systems. The mixed pixel/multipath interference problem arises from the violation of a standard range-imaging assumption that each pixel integrates over only a single, discrete backscattering source. While a numerical inversion method has previously been proposed, no close-form inverses have previously been posited. The first new method models reflectivity as a Cauchy distribution over range and uses four measurements at different modulation frequencies to determine the amplitude, phase and reflectivity distribution of up to two component returns within each pixel. The second new method uses attenuation ratios to determine the amplitude and phase of up to two component returns within each pixel. The methods are tested on both simulated and real data and shown to produce a significant improvement in overall error. While this paper focusses on the AMCW mixed pixel/multipath interference problem, the algorithms contained herein have applicability to the reconstruction of a sparse one dimensional signal from an extremely limited number of discrete samples of its Fourier transform

Extracting More Data from LiDAR in Forested Areas by Analyzing Waveform Shape

Light Detection And Ranging (LiDAR) in forested areas is used for constructing Digital Terrain Models (DTMs), estimating biomass carbon and timber volume and estimating foliage distribution as an indicator of tree growth and health. All of these purposes are hindered by the inability to distinguish the source of returns as foliage, stems, understorey and the ground except by their relative positions. The ability to separate these returns would improve all analyses significantly. Furthermore, waveform metrics providing information on foliage density could improve forest health and growth estimates. In this study, the potential to use waveform LiDAR was investigated. Aerial waveform LiDAR data were acquired for a New Zealand radiata pine plantation forest, and Leaf Area Density (LAD) was measured in the field. Waveform peaks with a good signal-to-noise ratio were analyzed and each described with a Gaussian peak height, half-height width, and an exponential decay constant. All parameters varied substantially across all surface types, ruling out the potential to determine source characteristics for individual returns, particularly those with a lower signal-to-noise ratio. However, pulses on the ground on average had a greater intensity, decay constant and a narrower peak than returns from coniferous foliage. When spatially averaged, canopy foliage density (measured as LAD) varied significantly, and was found to be most highly correlated with the volume-average exponential decay rate. A simple model based on the Beer-Lambert law is proposed to explain this relationship, and proposes waveform decay rates as a new metric that is less affected by shadowing than intensity-based metrics. This correlation began to fail when peaks with poorer curve fits were included

Airborne LiDAR for DEM generation: some critical issues

Airborne LiDAR is one of the most effective and reliable means of terrain data collection. Using LiDAR data for DEM generation is becoming a standard practice in spatial related areas. However, the effective processing of the raw LiDAR data and the generation of an efficient and high-quality DEM remain big challenges. This paper reviews the recent advances of airborne LiDAR systems and the use of LiDAR data for DEM generation, with special focus on LiDAR data filters, interpolation methods, DEM resolution, and LiDAR data reduction. Separating LiDAR points into ground and non-ground is the most critical and difficult step for DEM generation from LiDAR data. Commonly used and most recently developed LiDAR filtering methods are presented. Interpolation methods and choices of suitable interpolator and DEM resolution for LiDAR DEM generation are discussed in detail. In order to reduce the data redundancy and increase the efficiency in terms of storage and manipulation, LiDAR data reduction is required in the process of DEM generation. Feature specific elements such as breaklines contribute significantly to DEM quality. Therefore, data reduction should be conducted in such a way that critical elements are kept while less important elements are removed. Given the highdensity characteristic of LiDAR data, breaklines can be directly extracted from LiDAR data. Extraction of breaklines and integration of the breaklines into DEM generation are presented

Computational multi-depth single-photon imaging

We present an imaging framework that is able to accurately reconstruct multiple depths at individual pixels from single-photon observations. Our active imaging method models the single-photon detection statistics from multiple reflectors within a pixel, and it also exploits the fact that a multi-depth profile at each pixel can be expressed as a sparse signal. We interpret the multi-depth reconstruction problem as a sparse deconvolution problem using single-photon observations, create a convex problem through discretization and relaxation, and use a modified iterative shrinkage-thresholding algorithm to efficiently solve for the optimal multi-depth solution. We experimentally demonstrate that the proposed framework is able to accurately reconstruct the depth features of an object that is behind a partially-reflecting scatterer and 4 m away from the imager with root mean-square error of 11 cm, using only 19 signal photon detections per pixel in the presence of moderate background light. In terms of root mean-square error, this is a factor of 4.2 improvement over the conventional method of Gaussian-mixture fitting for multi-depth recovery.This material is based upon work supported in part by a Samsung Scholarship, the US National Science Foundation under Grant No. 1422034, and the MIT Lincoln Laboratory Advanced Concepts Committee. We thank Dheera Venkatraman for his assistance with the experiments. (Samsung Scholarship; 1422034 - US National Science Foundation; MIT Lincoln Laboratory Advanced Concepts Committee)Accepted manuscrip

Extending AMCW lidar depth-of-field using a coded aperture

By augmenting a high resolution full-field Amplitude Modulated Continuous Wave lidar system with a coded aperture, we show that depth-of-field can be extended using explicit, albeit blurred, range data to determine PSF scale. Because complex domain range-images contain explicit range information, the aperture design is unconstrained by the necessity for range determination by depth-from-defocus. The coded aperture design is shown to improve restoration quality over a circular aperture. A proof-of-concept algorithm using dynamic PSF determination and spatially variant Landweber iterations is developed and using an empirically sampled point spread function is shown to work in cases without serious multipath interference or high phase complexity

Multiple return separation for a full-field ranger via continuous waveform modelling

We present two novel Poisson noise Maximum Likelihood based methods for identifying the individual returns within mixed pixels for Amplitude Modulated Continuous Wave rangers. These methods use the convolutional relationship between signal returns and the recorded data to determine the number, range and intensity of returns within a pixel. One method relies on a continuous piecewise truncated-triangle model for the beat waveform and the other on linear interpolation between translated versions of a sampled waveform. In the single return case both methods provide an improvement in ranging precision over standard Fourier transform based methods and a decrease in overall error in almost every case. We find that it is possible to discriminate between two light sources within a pixel, but local minima and scattered light have a significant impact on ranging precision. Discrimination of two returns requires the ability to take samples at less than 90 phase shifts

A Signal processing approach for preprocessing and 3d analysis of airborne small-footprint full waveform lidar data

The extraction of structural object metrics from a next generation remote sensing modality, namely waveform light detection and ranging (LiDAR), has garnered increasing interest from the remote sensing research community. However, a number of challenges need to be addressed before structural or 3D vegetation modeling can be accomplished. These include proper processing of complex, often off-nadir waveform signals, extraction of relevant waveform parameters that relate to vegetation structure, and from a quantitative modeling perspective, 3D rendering of a vegetation object from LiDAR waveforms. Three corresponding, broad research objectives therefore were addressed in this dissertation. Firstly, the raw incoming LiDAR waveform typically exhibits a stretched, misaligned, and relatively distorted character. A robust signal preprocessing chain for LiDAR waveform calibration, which includes noise reduction, deconvolution, waveform registration, and angular rectification is presented. This preprocessing chain was validated using both simulated waveform data of high fidelity 3D vegetation models, which were derived via the Digital Imaging and Remote Sensing Image Generation (DIRSIG) modeling environment and real small-footprint waveform LiDAR data, collected by the Carnegie Airborne Observatory (CAO) in a savanna region of South Africa. Results showed that the preprocessing approach significantly increased our ability to recover the temporal signal resolution, and resulted in improved waveform-based vegetation biomass estimation. Secondly, a model for savanna vegetation biomass was derived using the resultant processed waveform data and by decoding the waveform in terms of feature metrics for woody and herbaceous biomass estimation. The results confirmed that small-footprint waveform LiDAR data have significant potential in the case of this application. Finally, a 3D image clustering-based waveform LiDAR inversion model was developed for 1st order (principal branch level) 3D tree reconstruction in both leaf-off and leaf-on conditions. These outputs not only contribute to the visualization of complex tree structures, but also benefit efforts related to the quantification of vegetation structure for natural resource applications from waveform LiDAR data

Spectral unmixing of Multispectral Lidar signals

In this paper, we present a Bayesian approach for spectral unmixing of multispectral Lidar (MSL) data associated with surface reflection from targeted surfaces composed of several known materials. The problem addressed is the estimation of the positions and area distribution of each material. In the Bayesian framework, appropriate prior distributions are assigned to the unknown model parameters and a Markov chain Monte Carlo method is used to sample the resulting posterior distribution. The performance of the proposed algorithm is evaluated using synthetic MSL signals, for which single and multi-layered models are derived. To evaluate the expected estimation performance associated with MSL signal analysis, a Cramer-Rao lower bound associated with model considered is also derived, and compared with the experimental data. Both the theoretical lower bound and the experimental analysis will be of primary assistance in future instrument design

A Few Photons Among Many: Unmixing Signal and Noise for Photon-Efficient Active Imaging

Conventional LIDAR systems require hundreds or thousands of photon detections to form accurate depth and reflectivity images. Recent photon-efficient computational imaging methods are remarkably effective with only 1.0 to 3.0 detected photons per pixel, but they are not demonstrated at signal-to-background ratio (SBR) below 1.0 because their imaging accuracies degrade significantly in the presence of high background noise. We introduce a new approach to depth and reflectivity estimation that focuses on unmixing contributions from signal and noise sources. At each pixel in an image, short-duration range gates are adaptively determined and applied to remove detections likely to be due to noise. For pixels with too few detections to perform this censoring accurately, we borrow data from neighboring pixels to improve depth estimates, where the neighborhood formation is also adaptive to scene content. Algorithm performance is demonstrated on experimental data at varying levels of noise. Results show improved performance of both reflectivity and depth estimates over state-of-the-art methods, especially at low signal-to-background ratios. In particular, accurate imaging is demonstrated with SBR as low as 0.04. This validation of a photon-efficient, noise-tolerant method demonstrates the viability of rapid, long-range, and low-power LIDAR imaging

The Fundamentals of Radar with Applications to Autonomous Vehicles

Radar systems can be extremely useful for applications in autonomous vehicles. This paper seeks to show how radar systems function and how they can apply to improve autonomous vehicles. First, the basics of radar systems are presented to introduce the basic terminology involved with radar. Then, the topic of phased arrays is presented because of their application to autonomous vehicles. The topic of digital signal processing is also discussed because of its importance for all modern radar systems. Finally, examples of radar systems based on the presented knowledge are discussed to illustrate the effectiveness of radar systems in autonomous vehicles