Patch-based holographic image sensing. (English) Zbl 1479.94017
In [A. M. Bruckstein et al., Appl. Comput. Harmon. Anal. 49, No. 1, 296–315 (2020; Zbl 1437.62698)], the authors proposed a method for image transmission, where image is transferred by packets which all carry a filtered sparse representation of the whole image (like holograms); this enables progressive recovery, improving the received image as more packets become available (independent of order of arrival). Here, the method is generalized to patch-based transform of several images simultaneously. Images are considered as ensembles of smaller patches produced by a random process; the design of image patches is based on distributed projections exploiting joint statistical properties of all the images, ensuring best packetsage recovery using the Wiener filter with the \(l_2\) (or Manhattan) norm. In the paper, mathematical analysis of the process, several visual examples of recovered (color) images and statistical properties of the recovery process are presented. The authors emphasize that the quality of recovery depends on the number of available packets and not on the order in which they arrive and share a basic implementation software written in Python 2.
Reviewer: Jaak Henno (Tallinn)
MSC:
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
| 94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
| 60G35 | Signal detection and filtering (aspects of stochastic processes) |
| 68U10 | Computing methodologies for image processing |
Keywords:
holographic representation; mean squared error estimation; stochastic image data; Wiener filterCitations:
Zbl 1437.62698References:
| [1] | Matplotlib, https://github.com/matplotlib/matplotlib/tree/v2.2.4. |
| [2] | NumPy, https://numpy.org/. |
| [3] | N. Ahmed, T. Natarajan, and K. Rao, Discrete cosine transform, IEEE Trans. Comput., C-23 (1974), pp. 90-93. · Zbl 0273.65097 |
| [4] | A. Bruckstein, M. Ezerman, A. Fahreza, and S. Ling, Holographic sensing, Appl. Comput. Harmon. Anal., 49 (2020), pp. 296-315. · Zbl 1437.62698 |
| [5] | A. M. Bruckstein, R. J. Holt, and A. N. Netravali, Low discrepancy holographic image sampling, Int. J. Imaging Syst. Technol., 15 (2005), pp. 155-167. |
| [6] | A. M. Bruckstein, R. J. Holt, and A. N. Netravali, Holographic representations of images, IEEE Trans. Image Process., 7 (1998), pp. 1583-1597. |
| [7] | A. M. Bruckstein, R. J. Holt, and A. N. Netravali, On holographic transform compression of images, Int. J. Imaging Syst. Technol., 11 (2000), pp. 292-314. |
| [8] | Y. Dar and A. M. Bruckstein, Benefiting from duplicates of compressed data: Shift-based holographic compression of images, J. Math. Imaging Vis. (2021), https://doi.org/10.1007/s10851-020-01003-1. · Zbl 1517.94018 |
| [9] | S. Dolev and S. Frenkel, Multiplication free holographic coding, in proceedings of the IEEE 26th Convention of Electrical and Electronics Engineers in Israel, 2010, pp. 146-150. |
| [10] | S. Dolev, S. L. Frenkel, and A. Cohen, Holographic coding by Walsh-Hadamard transformation of randomized and permuted data, Inform. Appl., 6 (2012), pp. 76-83. |
| [11] | R. Dovgard, Holographic image representation with reduced aliasing and noise effects, IEEE Trans. Image Process., 13 (2004), pp. 867-872. |
| [12] | V. K. Goyal, J. Kovačević, R. Arean, and M. Vetterli, Multiple description transform coding of images, in Proceedings of ICIP98, Vol. 1, 1998, pp. 674-678. |
| [13] | V. K. Goyal, J. Kovačević, and J. A. Kelner, Quantized frame expansions with erasures, Appl. Comput. Harmon. Anal., 10 (2001), pp. 203-233. · Zbl 0992.94009 |
| [14] | J. D. Hunter, Matplotlib: A 2D graphics environment, Comput. Sci. Eng., 9 (2007), pp. 90-95. |
| [15] | G. Kutyniok, A. Pezeshki, R. Calderbank, and T. Liu, Robust dimension reduction, fusion frames, and Grassmannian packings, Appl. Comput. Harmon. Anal., 26 (2009), pp. 64-76. · Zbl 1283.42046 |
| [16] | F. Lundh, A. Clark, and Contributors, Pillow, the Friendly PIL Fork, https://python-pillow.org/. |
| [17] | T. E. Oliphant, A Guide to NumPy, Vol. 1, Trelgol Publishing USA, 2006. |
| [18] | S. Pradhan, R. Puri, and K. Ramchandran, \(n\)-Channel symmetric multiple descriptions-Part I: \((n,k)\) source-channel erasure codes, IEEE Trans. Inform. Theory, 50 (2004), pp. 47-61. · Zbl 1301.94066 |
| [19] | R. Puri, S. Pradhan, and K. Ramchandran, \(n\)-Channel symmetric multiple descriptions-Part II: An achievable rate-distortion region, IEEE Trans. Inform. Theory, 51 (2005), pp. 1377-1392. · Zbl 1309.94093 |
| [20] | S. D. Servetto, K. Ramchandran, V. A. Vaishampayan, and K. Nahrstedt, Multiple description wavelet based image coding, IEEE Trans. Image Process., 9 (2000), pp. 813-826. |
| [21] | V. Vaishampayan, Design of multiple description scalar quantizers, IEEE Trans. Inform. Theory, 39 (1993), pp. 821-834. · Zbl 0784.94009 |
| [22] | R. Venkataramani, G. Kramer, and V. Goyal, Multiple description coding with many channels, IEEE Trans. Inform. Theory, 49 (2003), pp. 2106-2114. · Zbl 1301.94073 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
