I finally managed to find some time to update my publications list with papers that appeared near the end of the summer. The first set of papers extends our work on signal representations and embeddings and reinforces the importance of embeddings in signal representation applications.
As I have mentioned before, embeddings have been proven very powerful for encoding signal distances, with many applications in signal-based retrieval. In [1, 2] we explore these embeddings further. Their most exciting property is their information scalability. That means that their complexity scales according to the complexity of information required in the application. Using higher dimensions and more bits, we can represent a signal with little distortion. Using fewer dimensions and fewer bits, we can represent only the distances of signals up to a radius, but not the signals themselves.
The first paper [1] extends our earlier work on quantized Johnson-Lindenstrauss (J-L) embeddings [3] and demonstrates the importance of embeddings in cloud-based image retrieval. Specifically, we have extended our approach to handle retrieval using l1 distances and applied it to a face recognition database. While it has been proven that embeddings preserving l1 distances are not possible in general, we have managed to show that under certain circumstances l1 distance can exactly or approximately be mapped onto an l2 space, which can then be embedded using standard J-L tools.
The second paper [2] extends my SampTA and SPARS papers on phase embeddings [4, 5] by studying the effect of quantization. Phase embeddings preserve angles (correlations) of signals using the phase of a complex linear projection. Since the phase is uniformly distributed and bounded, it is very easy to design an optimal scalar quantizer for this embedding. However, given a fixed bit-rate, there is a trade-off between the dimensionality of the projection and the bits used to represent each coefficient. Navigating this trade-off is application dependent and not straightforward. The SPIE Wavelets and Sparsity XV paper [2] discusses this trade-off.
| [1] |
S. Rane, P. T. Boufounos, and A. Vetro, “Quantized Embeddings: An Efficient and Universal Nearest Neighbor Method for Cloud-based Image Retrieval,” Proc. SPIE Applications of Digital Image Processing XXXVI, no. 8856, San Diego, CA, August 25-29, 2013. |
| [2] |
P. T. Boufounos, “Angle-preserving Quantized Phase Embeddings,” Proc. SPIE Wavelets and Sparsity XV, no. 8858, San Diego, CA, August 25-29, 2013. |
| [3] |
M. Li, S. Rane, and P. T. Boufounos, “Quantized embeddings of scale-invariant image features for mobile augmented reality,” IEEE 14th International Workshop on Multimedia Signal Processing (MMSP), Banff, Canada, Sept. 17-19, 2012, Top 10% paper award. |
| [4] |
P. T. Boufounos, “On Embedding The Angles Between Signals,” Proc. Signal Processing with Adaptive Sparse Structured Representations (SPARS), Lausanne, Switzerland, July 8-11, 2013. |
| [5] |
P. T. Boufounos, “Sparse Signal Reconstruction from Phase-only Measurements,” Proc. Int. Conf. Sampling Theory and Applications (SampTA), Bremen, Germany, July 1-5, 2013. |