Super-Resolution Model for a Compressed-Sensing Measurement Setup

In this paper, we present a new compressed-sensing (CS) setup together with a new scalable CS model, which allows the tradeoff between system complexity (number of detectors) and time (number of measurements). We describe the calibration of the system with respect to model parameters and show the reconstruction of compressed measurements according to the new model, which are acquired with the proposed setup. The proposed model and its parameter are evaluated with the established measures, i.e., restricted isometry property and coherence. The resulting consequences for usable sparsifying basis are derived on this evaluation. With the proposed setup, it is possible to acquire high-resolution images with a low-resolution camera.

[1]  Janne Heikkilä,et al.  Geometric Camera Calibration Using Circular Control Points , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  Wei Lu,et al.  Modified-CS: Modifying compressive sensing for problems with partially known support , 2009, 2009 IEEE International Symposium on Information Theory.

[3]  E. Candès.  The restricted isometry property and its implications for compressed sensing , 2008 .

[4]  Alfred Mertins,et al.  Parameter calibration of a novel super-resolution model for a compressed-sensing measurement setup , 2011, 2011 IEEE International Instrumentation and Measurement Technology Conference.

[5]  Richard G. Baraniuk,et al.  An Information-Theoretic Approach to Distributed Compressed Sensing ∗ , 2005 .

[6]  François-Xavier Le Dimet,et al.  Deblurring From Highly Incomplete Measurements for Remote Sensing , 2009, IEEE Transactions on Geoscience and Remote Sensing.

[7]  Michael Elad,et al.  Stable recovery of sparse overcomplete representations in the presence of noise , 2006, IEEE Transactions on Information Theory.

[8]  Deanna Needell,et al.  CoSaMP: Iterative signal recovery from incomplete and inaccurate samples , 2008, ArXiv.

[9]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[10]  Balas K. Natarajan,et al.  Sparse Approximate Solutions to Linear Systems , 1995, SIAM J. Comput..

[11]  D. Donoho,et al.  Sparse MRI: The application of compressed sensing for rapid MR imaging , 2007, Magnetic resonance in medicine.

[12]  Ting Sun,et al.  Single-pixel imaging via compressive sampling , 2008, IEEE Signal Process. Mag..

[13]  Xiaoming Huo,et al.  Uncertainty principles and ideal atomic decomposition , 2001, IEEE Trans. Inf. Theory.

[14]  Jianwei Ma,et al.  Extensions of Compressed Imaging: Flying Sensor, Coded Mask, and Fast Decoding , 2011, IEEE Transactions on Instrumentation and Measurement.

[15]  Bernhard P. Wrobel,et al.  Multiple View Geometry in Computer Vision , 2001 .

[16]  Jitendra Malik,et al.  A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[17]  Wai Lam Chan,et al.  A single-pixel terahertz imaging system based on compressed sensing , 2008 .

[18]  Pierre Vandergheynst,et al.  Compressed Sensing and Redundant Dictionaries , 2007, IEEE Transactions on Information Theory.

[19]  Jared Tanner,et al.  Phase Transitions for Greedy Sparse Approximation Algorithms , 2010, ArXiv.

[20]  G. Peyré,et al.  A numerical exploration of compressed sampling recovery , 2010 .

[21]  Anthony Griffin,et al.  Compressed sensing of audio signals using multiple sensors , 2008, 2008 16th European Signal Processing Conference.

[22]  Thomas S. Huang,et al.  Image super-resolution as sparse representation of raw image patches , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[23]  Abdorreza Heidari,et al.  A 2D camera design with a single-pixel detector , 2009, 2009 34th International Conference on Infrared, Millimeter, and Terahertz Waves.