Publications by Year: 2007

Y. M. Lu and M. N. Do, “Sampling signals from a union of shift-invariance subspaces,” in Proc. SPIE Conf. on Wavelets Applications in Signal and Image Processing XII, San Diego, CA, 2007.
Y. M. Lu and M. N. Do, “Multidimensional Directional Filter Banks and Surfacelets,” IEEE Transactions on Image Processing, vol. 16, no. 4, pp. 918-931, 2007. MATLAB and C++ codeAbstract

In 1992, Bamberger and Smith proposed the directional filter bank (DFB) for an efficient directional decomposition of 2-D signals. Due to the nonseparable nature of the system, extending the DFB to higher dimensions while still retaining its attractive features is a challenging and previously unsolved problem. We propose a new family of filter banks, named NDFB, that can achieve the directional decomposition of arbitrary  N-dimensional (N >= 2) signals with a simple and efficient tree-structured construction. In 3-D, the ideal passbands of the proposed NDFB are rectangular-based pyramids radiating out from the origin at different orientations and tiling the entire frequency space. The proposed NDFB achieves perfect reconstruction via an iterated filter bank with a redundancy factor of in N-D. The angular resolution of the proposed NDFB can be iteratively refined by invoking more levels of decomposition through a simple expansion rule. By combining the NDFB with a new multiscale pyramid, we propose the surfacelet transform, which can be used to efficiently capture and represent surface-like singularities in multidimensional data.

M. Yan, et al., “Automatic detection of pelvic lymph nodes using multiple MR sequences,” in Proc. SPIE Conference on Medical Imaging, San Diego, 2007.
Y. M. Lu and M. N. Do, “Finding optimal integral sampling lattices for a given frequency support in multidimensions,” in Proc. IEEE International Conference on Image Processing, San Antonio, USA, 2007.Abstract

The search for alias-free sampling lattices for a given frequency support, in particular those lattices achieving minimum sam- pling densities, is a fundamental issue in various applications of signal and image processing. In this paper, we propose an efficient computational procedure to find all alias-free integral sampling lattices for a given frequency support with minimum sampling density. Central to this algorithm is a novel condition linking the alias-free sampling with the Fourier transform of the indicator function defined on the frequency support. We study the computation of these Fourier transforms based on the diver- gence theorem, and propose a simple closed-form formula for a fairly general class of support regions consisting of arbitrary N -dimensional polytopes, with polygons in 2-D and polyhedra in 3-D as special cases. The proposed algorithm can be useful in a variety of applications involving the design of efficient ac- quisition schemes for multidimensional bandlimited signals.


(This paper received one of the four available Student Paper Awards of ICIP.)

N. Mueller, Y. Lu, and M. N. Do, “Image interpolation using multiscale geometric representations,” in Proc. SPIE Conf. on Electronic Imaging, San Jose, USA, 2007.Abstract

With the ever increasing computational power of modern day processors, it has become feasible to use more robust and computationally complex algorithms that increase the resolution of images without distorting edges and contours. We present a novel image interpolation algorithm that uses the new contourlet transform to improve the regularity of object boundaries in the generated images. By using a simple wavelet-based linear interpolation scheme as our initial estimate, we use an iterative projection process based on two constraints to drive our solution towards an improved high-resolution image. Our experimental results show that our new algorithm significantly outperforms linear interpolation in subjective quality, and in most cases, in terms of PSNR as well.