Guided signal reconstruction with application to image magnification

We study the problem of reconstructing a signal from its projection on a subspace. The proposed signal reconstruction algorithms utilize a guiding subspace that represents desired properties of reconstructed signals. We show that optimal reconstructed signals belong to a convex bounded set, called the "reconstruction" set. We also develop iterative algorithms, based on conjugate gradient methods, to approximate optimal reconstructions with low memory and computational costs. The effectiveness of the proposed approach is demonstrated for image magnification, where the reconstructed image quality is shown to exceed that of consistent and generalized reconstruction schemes.

[2]  Michael Unser,et al.  Consistent Sampling and Signal Recovery , 2007, IEEE Transactions on Signal Processing.

[3]  W. Bastiaan Kleijn,et al.  On the mutual information between frequency bands in speech , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[4]  Hynek Hermansky,et al.  Beyond NYQUIST: towards the recovery of broad-bandwidth speech from narrow-bandwidth speech , 1995, EUROSPEECH.

[5]  Antonio Ortega,et al.  Towards a sampling theorem for signals on arbitrary graphs , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[6]  Hiroshi Yasukawa.  Signal restoration of broad band speech using nonlinear processing , 1996, 1996 8th European Signal Processing Conference (EUSIPCO 1996).

[7]  G. Miet,et al.  Speech enhancement via frequency bandwidth extension using line spectral frequencies , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[8]  Antonio Ortega,et al.  Active semi-supervised learning using sampling theory for graph signals , 2014, KDD.

[9]  Sunil K. Narang,et al.  Localized iterative methods for interpolation in graph structured data , 2013, 2013 IEEE Global Conference on Signal and Information Processing.

[10]  Bhiksha Raj,et al.  Bandwidth expansion of narrowband speech using non-negative matrix factorization , 2005, INTERSPEECH.

[11]  Michael Unser,et al.  A general sampling theory for nonideal acquisition devices , 1994, IEEE Trans. Signal Process..

[12]  H. Sebastian Seung,et al.  Learning the parts of objects by non-negative matrix factorization , 1999, Nature.

[13]  Yonina C. Eldar.  Sampling with Arbitrary Sampling and Reconstruction Spaces and Oblique Dual Frame Vectors , 2003 .

[14]  Ben Adcock,et al.  A Generalized Sampling Theorem for Stable Reconstructions in Arbitrary Bases , 2010, 1007.1852.

[15]  Douglas D. O'Shaughnessy,et al.  Statistical recovery of wideband speech from narrowband speech , 1992, IEEE Trans. Speech Audio Process..

[16]  Yonina C. Eldar,et al.  A minimum squared-error framework for generalized sampling , 2006, IEEE Transactions on Signal Processing.

[17]  Moon Gi Kang,et al.  Super-resolution image reconstruction: a technical overview , 2003, IEEE Signal Process. Mag..

[18]  Takayuki Nagai,et al.  Speech signal band width extension and noise removal using subband HMN , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.