Chun-Lin Liu – Topics – Others

• Toolkit for coarray MUSIC and coarray interpolation

• Sparse array design with reduced mutual coupling

  • Super nested arrays (1-D)

  • Hourglass arrays (2-D)

• Cramér-Rao bounds for sparse arrays

• Others

Linear Canonical Transforms (LCTs)

Linear canonical transforms based on eigen-decompositions. (View larger)

The linear canonical transform (LCT) is an integral transform that finds many applications in optics, quantum mechanics, and signal processing. LCTs own parameter , , , , and thus unify the Fourier transform, the fractional Fourier transform, the Fresnel transform, the scaling operation, and the chirp multiplication operation.

My research interest on the LCT is the discrete implementation methods by proper decompositions on the LCT.

Our Papers

1. S.-C. Pei and C.-L. Liu, ‘‘Differential Commuting Operator and Closed-form Eigenfunctions for Linear Canonical Transforms,’’ Journal of the Optical Society of America A (JOSA A), vol. 30, issue 10, pp. 2096-2110, Oct. 2013.
   (DOI)

2. S.-C. Pei, C.-L. Liu, and Y.-C. Lai, ‘‘The Generalized Fractional Fourier Transform,’’ in Proc. of 2012 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP 2012), pp. 3705-3708, Kyoto, Japan, Mar. 2012.
   (DOI) (Full text) (Poster)

Discrete Spherical Harmonic Oscillator Transforms (Discrete SHOTs)

3D object reconstruction using DSHOTs (View larger)

The spherical harmonic oscillator transforms originate from the wavefunction of the 3D isotropic harmonic oscillator system. It was found that the spherical harmonic oscillator wavefunctions (SHOWs) can be obtained from the finite linear combination of the separable Hermite Gaussian functions, which are defined on the Cartesian coordinates. The corresponding transform, called the spherical harmonic oscillator transforms (SHOTs), can also be expressed in terms of the separate Hermite transforms.

We applied the SHOWs and the SHOTs to the field of signal processing. A fast computation algorithm on the combination coefficients was proposed and the SHOTs were utilized to many applications, including the eigenfunctions of 3D DFT, signal expansion and reconstruction, rotational invariance feature analysis, and 3D MRI data compression.

Our Papers

1. S.-C. Pei, C.-L. Liu, and Y.-C. Lai, ‘‘Discrete Laguerre Gaussian Transforms and Their Applications,’’ IEEE Trans. on Signal Processing, vol. 64, no. 12, pp. 3156-3166, Apr. 2016.
   (DOI)

2. S.-C. Pei and C.-L. Liu, ‘‘Discrete Spherical Harmonic Oscillator Transforms on the Cartesian Grids Using Transformation Coefficients,’’ IEEE Trans. on Signal Processing, vol. 61, no. 5, pp. 1149-1164, Mar. 2013.
   (DOI)
   This paper was on the front cover of IEEE TSP.

3. S.-C. Pei and C.-L. Liu, ‘‘3D Rotation Estimation Using Discrete Spherical Harmonic Oscillator Transforms,’’ in Proc. of 2014 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP 2014), pp. 774-778, Florence, Italy, May 2014.
   (DOI) (Full text) (Slides)

4. S.-C. Pei and C.-L. Liu, ‘‘A General Form of 2D Fourier Transform Eigenfunctions,’’ in Proc. of 2012 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP 2012), pp. 3701-3704, Kyoto, Japan, Mar. 2012.
   (DOI) (Full text) (Poster)