Information Content in Uniformly Discretized Gaussian Noise: Optimal Compression Rates

Romeo, August; Gaztañaga, E.; Barriga, J.; Elizalde, E.

doi:10.1142/s0129183199000528

Cited by 5 publications

(7 citation statements)

References 14 publications

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“…Resuming what discussed in Romeo et al (1999), Maris et al (2000a), Gaztañaga et al (2000), and Gaztañaga et al (2001) and using the formalism introduced in Maris et al (2000a), the maximum compression rate, C r , achievable by any lossless compression method for any digitized signal represented by integers of N bits bits and with Shannon's entropy H is (Nelson & Gailly 1996) …”

Section: Discussionmentioning

confidence: 99%

“…As amply discussed in Romeo et al (1999), Maris et al (2000a), Gaztañaga et al (2000) and Gaztañaga et al (2001) in the case of CMB data, the output of the acquisition chain is white-noise dominated. Taking as a representative case P/LFI, the best compression rate, C r , achievable by compressing the output of the acquisition chain, even in the case of an ideal compressor, is C r < 2.7, to be compared with a required C r > ∼ 8.…”

Section: Introductionmentioning

confidence: 99%

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The effect of signal digitisation in CMB experiments

Maris

Maino

Burigana

et al. 2004

A&A

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Abstract. Signal digitisation may produce significant effects in balloon -borne or space CMB experiments, when the limited bandwidth for downlink of data requires loss-less data compression. In fact, the data compressibility depends on the quantization step q applied on board by the instrument acquisition chain. In this paper we present a study of the impact of the quantization error in CMB experiments using, as a working case, simulated data from the P/LFI 30 and 100 GHz channels. At TOD level, the effect of the quantization can be approximated as a source of nearly normally distributed noise, with RMS q/ √ 12N s , with deviations from normality becoming relevant for a relatively small number of repeated measures N s < ∼ 20. At map level, the data quantization alters the noise distribution and the expectation of some higher order moments. We find a constant ratio, 1/( √ 12σ/q), between the RMS of the quantization noise and RMS of the instrumental noise, σ over the map ( 0.14 for σ/q 2), while, for σ/q ∼ 2, the bias on the expectation for higher order moments is comparable to their sampling variances. Finally, we find that the quantization introduces a power excess, C ex , that, although related to the instrument and mission parameters, is weakly dependent on the multipole at middle and large and can be quite accurately subtracted. For σ/q 2, the residual uncertainty, ∆C ex , implied by this subtraction is only 1-2% of the RMS uncertainty, ∆C noise , on C sky reconstruction due to the noise power, C noise . Only for < ∼ 30 the quantization removal is less accurate; in fact, the 1/ f noise features, although efficiently removed, increase C noise , ∆C noise , C ex and then ∆C ex ; anyway, at low multipoles C sky ∆C noise > ∆C ex . This work is based on P LFI activities.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The effect of signal digitisation in CMB experiments

Maris

Maino

Burigana

et al. 2004

A&A

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“…For nearly-Gaussian probability distributions digitized to b bits per σ, the Shannon entropy is H ≈ log 2 √ 2πe + log 2 b(e.g. Romeo et al 1999). For b = 1 a numerical evaluation of the Shannon entropy shows that ≥ 2.1 bpp will be required.…”

Section: Codec Noisementioning

confidence: 99%

Noise and Bias In Square-Root Compression Schemes

Bernstein¹,

Bebek²,

Rhodes³

et al. 2010

PUBL ASTRON SOC PAC

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We investigate data compression schemes for proposed all-sky diffraction-limited visible/NIR sky surveys aimed at the dark energy problem. We show that lossy squareroot compression to 1 bit of noise per pixel, followed by standard lossless compression algorithms, reduces the images to 2.5-4 bits per pixel, depending primarily upon the level of cosmic-ray contamination of the images. Compression to this level adds noise equivalent to ≤ 10% penalty in observing time. We derive an analytic correction to flux biases inherent to the square-root compression scheme. Numerical tests on simple galaxy models confirm that galaxy fluxes and shapes are measured with systematic biases 10 −4 induced by the compression scheme, well below the requirements of supernova and weak gravitational lensing dark-energy experiments. An accompanying paper (Vanderveld et al. 2009) bounds the shape biases using realistic simulated images of the high-Galactic-latitude sky. The square-root preprocessing step has advantages over simple (linear) decimation when there are many bright objects or cosmic rays in the field, or when the background level will vary.

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“…The variations of the spectral index in different observations by XMM-Newton, ASCA and BeppoSAX suggest that the source undergoes a spectral transition similar to those in the other XRBs. The EGRET source 3EG J1639−4702 (Romero et al 1999) could be associated with the X-ray source considering the large position uncertainties. The infrared images from the 2MASS database and the optical observations indicate a bright and massive companion for the X-ray source .…”

Section: Igr J16318−4848: This Transient Source Was Discovered Bymentioning

confidence: 99%

GMRT observations of the field of INTEGRAL X-ray sources - I

Pandey

Manchanda²,

Rao

et al. 2006

A&A

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Since its launch the INTEGRAL observatory has discovered a variety of hard X-ray sources in the Galactic plane. Using GMRT, we have made repeated observations of these sources to search for the radio counterparts of seventeen of them at low frequencies. The source positions were taken from the various ATEL and IAUC announcements reporting their discovery. Possible radio counterparts for seven of these sources, IGR J06074+2205, IGR J15479−4529, IGR J16479−4514, IGR J17091−3624, IGR J18027−1455, IGR J18539+0727 and IGR J21247+5058 were detected within 3σ of the positional uncertainty derived from the INTEGRAL observations. The offset in the radio position was calculated using the positions mentioned in the ATEL. We have also analyzed the available NVSS images for some of these fields at 1.4 GHz along with our observations. In this paper we present the radio images and the best fit positions for the positive detections. The X-ray variability for some of the sources within the time scales of 100 s to 1 ks as seen in the RXTE/PCA light curves suggests their Galactic origin and possible binary nature. We discuss briefly the characteristics of these sources from the available information at different wave bands.

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Information Content in Uniformly Discretized Gaussian Noise: Optimal Compression Rates

Cited by 5 publications

References 14 publications

The effect of signal digitisation in CMB experiments

The effect of signal digitisation in CMB experiments

Noise and Bias In Square-Root Compression Schemes

GMRT observations of the field of INTEGRAL X-ray sources - I

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