Differential Privacy via Wavelet Transforms

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Calibrating Noise to Sensitivity in Private Data Analysis

Cynthia Dwork, Frank McSherry, Kobbi Nissim … (2006)

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Ideal Spatial Adaptation by Wavelet Shrinkage

David Donoho, Iain M. Johnstone (1994)

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Adaptive wavelet thresholding for image denoising and compression.

S.G. Chang, Bin Yu, M. Vetterli (2000)

The first part of this paper proposes an adaptive, data-driven threshold for image denoising via wavelet soft-thresholding. The threshold is derived in a Bayesian framework, and the prior used on the wavelet coefficients is the generalized Gaussian distribution (GGD) widely used in image processing applications. The proposed threshold is simple and closed-form, and it is adaptive to each subband because it depends on data-driven estimates of the parameters. Experimental results show that the proposed method, called BayesShrink, is typically within 5% of the MSE of the best soft-thresholding benchmark with the image assumed known. It also outperforms SureShrink (Donoho and Johnstone 1994, 1995; Donoho 1995) most of the time. The second part of the paper attempts to further validate claims that lossy compression can be used for denoising. The BayesShrink threshold can aid in the parameter selection of a coder designed with the intention of denoising, and thus achieving simultaneous denoising and compression. Specifically, the zero-zone in the quantization step of compression is analogous to the threshold value in the thresholding function. The remaining coder design parameters are chosen based on a criterion derived from Rissanen's minimum description length (MDL) principle. Experiments show that this compression method does indeed remove noise significantly, especially for large noise power. However, it introduces quantization noise and should be used only if bitrate were an additional concern to denoising.

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Title: IEEE Transactions on Knowledge and Data Engineering

Abbreviated Title: IEEE Trans. Knowl. Data Eng.

Publisher: Institute of Electrical and Electronics Engineers (IEEE)

ISSN (Print): 1041-4347

Publication date Created: August 2011

Publication date (Print): August 2011

Volume: 23

Issue: 8

Pages: 1200-1214

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DOI: 10.1109/TKDE.2010.247

SO-VID: 058765bc-e09d-498d-a69c-7832f39a705d

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Differential Privacy via Wavelet Transforms

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Big Data Privacy

Most cited references 27

Calibrating Noise to Sensitivity in Private Data Analysis

Ideal Spatial Adaptation by Wavelet Shrinkage

Adaptive wavelet thresholding for image denoising and compression.

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