Coded aperture compressive 3-D LIDAR

Question

1. What are the contributions in "Coded aperture compressive 3-d lidar" ?

2. What is the common signal model used for CS?

3. What is the truncation step of the model-based algorithm?

4. What principles are used to determine the depth of the scene?

Accepted Answer

In this paper the authors propose a new depth sensing architecture that exploits a fixed coded aperture to significantly reduce the number of sensors compared to conventional systems.. The authors further develop a modeling and reconstruction framework, based on model-based compressed sensing, which characterizes a large variety of depth sensing systems.

Accepted Answer

To capture structure, the most commonly used signal model is sparsity: the signal comprises a linear combination of very few atoms selected from a basis or a dictionary.

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The truncation step of their model-based algorithm incorporates a K-term truncation of s by first optimizing (8) to obtain a candidate depth map d, which corresponds to a candidate support set (nx, ny,dnx,ny ).

Accepted Answer

COMPRESSIVE LIDAR SENSINGFundamentally, the LIDAR architecture the authors propose relies on classical time-of-flight (TOF) LIDAR principles: a pulse is transmitted toilluminate the scene and the delayed reflections from each object in the scene are acquired by the system and used to determine the depth of each object.

Accepted Answer

Using compressive approaches, it has been shown that images can be acquired with measurements as few as 10% of the number of pixels NxNy .

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A CS-based acquisition system can be modeled asr = A(s), (1)where A(·) is a linear function, s belongs in some appropriate signal space, and r belongs in the measurement space.

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As long as such a projection can be computed, common greedy CS reconstruction algorithms, such as Compressive Sampling Matching Pursuit (CoSaMP) [19] and Iterative Hard Thresholding (IHT) [20], can be modified to reconstruct signals in the model.

Accepted Answer

The discretized received signal at sensor m, r ∈ RM,N ′ t canthen be computed as a sequence of linear transformationsr = S(M(P(s))) = A(s), (5)where P, M and S denote, respectively, the linear transformations due to the pulse, the mask of the coded aperture and the sampling of the optical field by the sensors.

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In their depth sensing problem, the authors map each vertex to represent a spatial location v = (nx, ny) of the scene, and each label to represents a discrete depth value lv = dnx,ny .

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The (`1) TV norm of a discrete map d ∈ RNx×Ny , is defined as‖d‖TV = ‖∇xd‖1 + ‖∇yd‖1, (6)where∇xd is the discrete gradient along direction x and ‖ ·‖1 is the element-wise `1 norm of a matrix, i.e.,‖∇xd‖1 = N∑ny=1 N−1∑ nx=1 ∣∣dnx,ny − dnx+1,ny ∣∣ , (7) with the y direction similarly defined.

Accepted Answer

the distance the pulse travels from the laser to the reflecting scene point and back to the sensor is 2d, corresponding to a pulse delay, i.e., TOF, τ = 2d/c, where c is the speed of light in the medium.

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two spatially adjacent non-zero coefficients of s—i.e., with respect to the nx and ny coordinates—should also have similar depth—i.e., nt coordinate—except for very few discontinuities.

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The discretization is such that each reflector can be assumed approximately flat and parallel to the sensor plane over the area of a pixel, such that the depth constraint is preserved in the discrete representation.

Accepted Answer

It is straightforward to show that with S = 1, the EMD constraint applied to s becomes a TV constraint on its support, i.e., on the depth map.

Coded aperture compressive 3-D LIDAR

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Most frequently asked questions

1. What are the contributions in "Coded aperture compressive 3-d lidar" ?

2. What is the common signal model used for CS?

3. What is the truncation step of the model-based algorithm?

4. What principles are used to determine the depth of the scene?

5. How many pixels can be acquired with compressive approaches?

6. What is the common CS-based acquisition system?

7. What is the way to reconstruct a signal?

8. What is the discretization of the received signal?

9. What is the energy function of the depth sensing problem?

10. What is the TV norm of a discrete map?

11. How long does the pulse travel from the laser to the reflecting scene point?

12. What is the definition of a s-based depth map?

13. What is the difference between the discretization of the pulse and the received signal?

14. What is the definition of a constraint on the TV?

Figures

Citations

Depth Sensing Using Geometrically Constrained Polarization Normals

Frequency-modulated continuous-wave LiDAR compressive depth-mapping.

Depth Sensing Using Geometrically Constrained Polarization Normals

A Sketching Framework for Reduced Data Transfer in Photon Counting Lidar

Taking Compressive Sensing to the Hardware Level: Breaking Fundamental Radio-Frequency Hardware Performance Tradeoffs

References

Compressed Sensing: Theory and Applications

Fast approximate energy minimization via graph cuts

Stable signal recovery from incomplete and inaccurate measurements

Stable Signal Recovery from Incomplete and Inaccurate Measurements

CoSaMP: Iterative signal recovery from incomplete and inaccurate samples

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