Applying the uniform resampling (URS) algorithm to a lissajous trajectory: Fast image reconstruction with optimal gridding

Moriguchi, Hisamoto; Duerk, Jeffrey L.

doi:10.1002/1522-2594(200011)44:5<766::aid-mrm15>3.0.co;2-c

Cited by 23 publications

(9 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In a Lissajous trajectory period ( ), assuming that is the sampling frequency, the sampling start time is and the end time is , the sampling scheme in ref. 28 can be summarized as Eq. ( 10 ), and the diagram of the sampling point cloud is shown in Fig.…”

Section: Resultsmentioning

confidence: 99%

“…With the trajectory of ref. 28 , we increase the sampling frequency by only twice to obtain the point cloud shown in Fig. 3b .…”

Section: Resultsmentioning

confidence: 99%

“…Moreover, spiral and rosette trajectory patterns support scanning mode with both axes 27 . However, the Lissajous trajectory has the special geometric characteristics necessary for the rapid reconstruction of nonrectilinear Cartesian k -space trajectories with constant sampling time intervals 28 . The Lissajous scheme is a time-efficient sampling scheme and is currently deployed in various fields.…”

Section: Introductionmentioning

confidence: 99%

“…Likes 43 proposed that the Lissajous trajectory was original, and its sampling density was studied by Hardy et al 44 . Moriguchi 28 demonstrated that the Lissajous curve has the feasibility of Cartesian gridding of sampling points with constant sampling time intervals, and when , , and the sampling frequency of the point cloud is 198 Hz, the point cloud satisfies the Cartesian grid. In ref.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Improved sampling scheme for LiDAR in Lissajous scanning mode

2022

View full text Add to dashboard Cite

MEMS light detection and ranging (LiDAR) is becoming an indispensable sensor in vehicle environment sensing systems due to its low cost and high performance. The beam scanning trajectory, sampling scheme and gridding are the key technologies of MEMS LiDAR imaging. In Lissajous scanning mode, this paper improves the sampling scheme, through which a denser Cartesian grid of point cloud data at the same scanning frequency can be obtained. By summarizing the rules of the Cartesian grid, a general sampling scheme independent of the beam scanning trajectory patterns is proposed. Simulation and experiment results show that compared with the existing sampling scheme, the resolution and the number of points per frame are both increased by 2 times with the same hardware configuration and scanning frequencies for a MEMS scanning mirror (MEMS-SM). This is beneficial for improving the point cloud imaging performance of MEMS LiDAR.

show abstract

Section: Resultsmentioning

confidence: 99%

“…With the trajectory of ref. 28 , we increase the sampling frequency by only twice to obtain the point cloud shown in Fig. 3b .…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Improved sampling scheme for LiDAR in Lissajous scanning mode

2022

View full text Add to dashboard Cite

show abstract

“…(1), the frequency difference between ω x and ω y determines the overall shape of the Lissajous pattern and the period in which the pattern progresses and repeats itself. 26,27 The phase difference between the sinusoids, which is assumed zero in this paper for simplicity, has also an impact on the shape of the pattern. 26 Numerous scan patterns can be generated by selecting frequencies and phase shifts of the two sinusoids in Eq.…”

Section: Lissajous Patternmentioning

confidence: 99%

High-speed Lissajous-scan atomic force microscopy: Scan pattern planning and control design issues

Bazaei

Yong²,

Moheimani³

2012

Review of Scientific Instruments

133

View full text Add to dashboard Cite

Tracking of triangular or sawtooth waveforms is a major difficulty for achieving high-speed operation in many scanning applications such as scanning probe microscopy. Such non-smooth waveforms contain high order harmonics of the scan frequency that can excite mechanical resonant modes of the positioning system, limiting the scan range and bandwidth. Hence, fast raster scanning often leads to image distortion. This paper proposes analysis and design methodologies for a nonlinear and smooth closed curve, known as Lissajous pattern, which allows much faster operations compared to the ordinary scan patterns. A simple closed-form measure is formulated for the image resolution of the Lissajous pattern. This enables us to systematically determine the scan parameters. Using internal model controllers (IMC), this non-raster scan method is implemented on a commercial atomic force microscope driven by a low resonance frequency positioning stage. To reduce the tracking errors due to actuator nonlinearities, higher order harmonic oscillators are included in the IMC controllers. This results in significant improvement compared to the traditional IMC method. It is shown that the proposed IMC controller achieves much better tracking performances compared to integral controllers when the noise rejection performances is a concern.

show abstract

Ultrafast imaging: Principles, pitfalls, solutions, and applications

Tsao

2010

Magnetic Resonance Imaging

View full text Add to dashboard Cite

Ultrafast MRI refers to efficient scan techniques that use a high percentage of the scan time for data acquisition. Often, they are used to achieve short scan duration ranging from sub-second to several seconds. Alternatively, they may form basic components of longer scans that may be more robust or have higher image quality. Several important applications use ultrafast imaging, including real-time dynamic imaging, myocardial perfusion imaging, high-resolution coronary imaging, functional neuroimaging, diffusion imaging, and whole-body scanning. Over the years, echo-planar imaging (EPI) and spiral imaging have been the main ultrafast techniques, and they will be the focus of the review. In practice, there are important challenges with these techniques, as it is easy to push imaging speed too far, resulting in images of a nondiagnostic quality. Thus, it is important to understand and balance the trade-off between speed and image quality. The purpose of this review is to describe how ultrafast imaging works, the potential pitfalls, current solutions to overcome the challenges, and the key applications.

show abstract

Applying the uniform resampling (URS) algorithm to a lissajous trajectory: Fast image reconstruction with optimal gridding

Cited by 23 publications

References 12 publications

Improved sampling scheme for LiDAR in Lissajous scanning mode

Improved sampling scheme for LiDAR in Lissajous scanning mode

High-speed Lissajous-scan atomic force microscopy: Scan pattern planning and control design issues

Ultrafast imaging: Principles, pitfalls, solutions, and applications

Contact Info

Product

Resources

About