Permanently shadowed locations at the lunar poles are potential sites for significant concentrations of cold-trapped volatiles, including water ice. Hydrogen enhancements are seen at the poles, but the physical form, abundance and distribution of this hydrogen remains controversial. Using a pixon-based image reconstruction algorithm to effectively improve spatial resolution, we derive maps of the lunar south polar water-equivalent hydrogen concentration that are fully consistent with the orbital neutron measurements, with abundances greater than 0.5 wt% in some permanently shadowed locations. This is much greater than the highest solar wind hydrogen abundance in returned lunar samples, and may indicate ice between regolith grains. If the hydrogen distribution is inhomogeneous within a permanently shadowed crater, then even higher abundances are implied. In Shackleton crater, for example, the derived count rates are consistent with 10% of the crater floor area having 20-wt% water-equivalent hydrogen, and the remainder at 0.25 wt%.
 For decades scientists have considered the possibility that water ice deposits may exist in permanently shaded craters near both lunar poles [Watson et al., 1961; Arnold, 1979]. Polar crater floors would be extremely cold (<70 K) [Vasavada et al., 1999], and a significant number of water molecules delivered by meteoritic infall can survive loss processes, find their way to these craters and be cold-trapped for billions of years [Butler, 1997]. Implanted solar wind hydrogen could yield impact-liberated water molecules, leading to concentrations as high as 4 wt% in polar shadow [Crider and Vondrak, 2003]. But the existence of cold-trapped water ice (and other volatiles) in permanently shadowed craters near the lunar poles continues to be very controversial. On one hand, the Lunar Prospector neutron spectrometer (LPNS) data strongly suggest the presence of polar hydrogen enhancements [Feldman et al., 1998, 2000, 2001; Lawrence et al., 2006], and anomalous bistatic radar returns from the Clementine lunar orbital mission have been interpreted in terms of icy materials [Nozette et al., 1996, 2001]. On the other hand, Earth-based radar imaging of the Moon has not revealed large, bright, depolarized features like those seen at Mercury [Stacy et al., 1997; Campbell et al., 2003]. The enhanced circular polarization ratios observed at the lunar poles by Earth-based radar are similar to those seen for crater ejecta and small-scale topographic relief at lower latitudes, where ice could not possibly exist [Campbell et al., 2006]. But cold-trapped ice residing in the spaces between regolith grains could amount to as much as several tens of percent by volume (up to ∼20% by weight); the radar backscatter technique cannot distinguish between ice in such a physical arrangement and ice-free blocky materials [Stacy et al., 1997; Campbell et al., 2003, 2006].
 Earlier LPNS estimates of 1.5 ± 0.8 wt% water-equivalent hydrogen (WEH) in permanently shadowed craters were based on (1) an assumed abundance of 110 ppm solar wind implanted hydrogen in non-shadowed regions, and (2) the locations and areas of the largest permanently shadowed south pole craters [Feldman et al., 1998, 2000, 2001]. Here we derive new estimates for the location and abundance of hydrogen enhancements at the lunar south pole. We apply advanced image deconvolution techniques to the neutron data, using a plausible model of permanent shadow to constrain the locations of possible ice deposits.
 We use the LPNS low-altitude (30-km mean altitude) dataset. The data have been corrected for cosmic ray variations, orbital altitude variations, and instrument gain changes [Maurice et al., 2004]. The 8-sec LPNS epithermal data are accumulated in a pole-centered grid of 5 × 5-km bins extending out to 600 km from the pole. Accumulated counts and time within each bin provide an estimate of epithermal count rate for that location. Owing to Lunar Prospector's polar orbit, bins near the pole have the highest sample density (168 samples/bin maximum) while those near the edge of the region of interest have the lowest (median 2 samples/bin at 595 km distance from the pole). The spatial sampling distribution bears importantly on the uncertainties in estimated epithermal count rate for each 5-km bin, and hence on the image reconstruction process.
2. South Pole Shadow Model
 We distinguish between areas that receive some sunlight over the course of a year, and those in true permanent shadow. The latter could host stably cold-trapped near-surface ice, whereas the former could not. But to firmly establish the locations of permanent shadow a complete and accurate digital elevation model (DEM) of the south pole is needed. The south pole DEMs derived from Earth-based radar [Margot et al., 1999], and Clementine stereo imaging [Cook et al., 2000; Bussey et al., 2003] are missing large areas due to coverage or winter lighting conditions. We combine the south pole radar DEM (resampled at 1 km) and the stereo DEM [Rosiek and Aeschliman, 2001; U.S. Geological Survey, 2002] to maximize coverage. We fill the gaps by interpolating a smoothly varying crater floor where such a model is appropriate, and otherwise fill with a smooth concave fit. We also incorporate 321 of the ≤20-km diameter craters identified by Bussey et al. , modifying the topography at their locations using the simple crater model of Pike  scaled to the crater diameter.
 Next, we calculate the maximum summertime south polar illumination by mapping the DEM onto a sphere of 1738 km radius, and determining what pixels are in view of the sun. A lunar spin axis tilt of 1.6° toward the sun and the finite 0.5° diameter of the sun's disk are applied as the Moon progresses through a lunation. At each phase step, we identify those pixels in sunlight and those in shadow. Pixels that never see the sun through a full summer lunation are labeled as permanently shadowed. Finally, a Clementine photomosaic (acquired during southern winter) is used to correct spuriously shadowed pixels [Bussey et al., 1999]. Our estimated locations of permanent shadow include the floors of Shackleton, Shoemaker, de Gerlache, Faustini and other craters. We rebin the 1-km shadow model in the LPNS 5-km grid in order to form a corresponding map. Since many 5-km bins contain both sunlit and shadowed 1-km pixels from the illumination model, we treat bins containing more than 50% shadow pixels as shadowed in their entirety. Bins having 50% or less shadowed pixels are considered sunlit. A total shadowed area of ∼12,150 km2 is obtained for the south polar region at 5-km resolution. The diameters and shadowed areas within six south pole craters are given in Table 1.
Table 1. South Pole Craters and Inferred WEH Abundances
 The observed LPNS epithermal neutron count rate map, O, can be modeled as a convolution of the instrument spatial response function, p, with the surface emission map, I, to which is added a noise model, N: O = pI + N ( denotes a convolution integral: pI = ∫p(x − y)I(y)dy). The information we seek is I. We have previously attempted to estimate I using a simple iterative van Cittert deconvolution technique with count rate constraints, which tends to amplify N in the process of estimating I [Elphic et al., 2005]. Here we employ a variant of the pixon image reconstruction technique, which is far less susceptible to noise amplification [Piña and Puetter, 1993; Puetter, 1995; Puetter and Yahil, 1999; Eke, 2001; Puetter et al., 2005].
 A pixon is a connected set of pixels, whose size is locally determined such that all pixons in the reconstructed image have the same information content [Piña and Puetter, 1993]. Every pixel in the estimated epithermal count rate map has a signal-to-noise ratio, and the pixons are sized to contain the required signal-to-noise. Thus, pixels far from the south pole, with fewer observations, will be gathered into larger pixons than pixels nearer to the pole. The approach seeks the smallest number of pixons that adequately fit the data given the measurement uncertainties, in effect capturing Ockham's razor. The pixon approach has been used successfully with Lunar Prospector thorium data to improve spatial resolution [Lawrence et al., 2007].
 We apply a further very powerful constraint: Areas that are considered sunlit (at least part of the time) are allowed to have no more than 0.25 wt% WEH (275 ppm [H], twice the maximum found in returned soil and regolith breccia samples [Haskin and Warren, 1991]). Pixels in permanent shadow can have more than 10 wt% WEH, if needed. The prior-knowledge in such an illumination/shadow map places limits on the allowed values of I at a higher resolution than the LPNS footprint. Of course, this constraint is only as good as our incomplete knowledge of lunar topography and lighting. Nevertheless, even approximate models of shadow will result in plausible models of surface hydrogen distribution, models that must (and do) agree with the orbital observations.
 To test the pixon algorithm, we created two simulated maps (not shown): (1) a single count rate (19.5 counts/sec) for all pixels, and (2) the locations of permanent shadow were assigned a WEH abundance of 0.4 wt% while non-shadowed pixels were assigned an abundance of 0.07 wt%. Poisson-distributed noise and LPNS spatial sampling were used to create both maps. Using the permanent shadow constraints, the pixon procedure recovered identical count rates within 0.03 counts/sec for both types of terrain in the first map, essentially determining that only one piece of information, a single count rate, adequately described the scene. For the second map, the procedure recovered different count rates for the sunlit and shadowed pixels. Depending on their location, size and signal-to-noise ratio, shadowed feature count rates ranged between 0.5 counts/sec below or above the model value. This count rate variability translates into 0.40 ± 0.07 wt% WEH for this test case.
4. Deconvolution Results
Figure 1a is a map of raw, 5 × 5-km binned epithermal count rate, C0, measured during the low-altitude (average 30 km) phase of the Lunar Prospector mission. Blue contour lines denote the boundaries of permanently shadowed regions, from the model in Section 2. Labeled features are the approximate rim of the highly degraded crater Cabaeus (“C”), de Gerlache (“dG”), Shackleton (“S”), Shoemaker (“Sh”), and Faustini (“F”). Figure 1b is the recovered epithermal count rate map, CP, with the same dynamic range as Figure 1a; the minimum count rate of 9 counts/sec corresponds to 2.8 wt% WEH.
 When the pixon-recovered model epithermal count rate map CP is convolved with the instrument response function p, it should agree with the measured epithermal map (unsmoothed) C0 within statistics. Figure 1c is a map of the reduced residuals given by (pCP − C0)/σ, where σ is the uncertainty in each 5 × 5 km pixel based on the original data. The color bar of Figure 1c ranges from −3 to +3 standard deviations. We expect nearly all (99.7%) of the reduced residuals to lie within these limits. Figure 1d is a histogram of the reduced residuals shown in Figure 1c; the histogram is overlain by a Gaussian curve with unity standard deviation and zero mean. The mean of the reduced residuals is 0.032 and the standard deviation is 1.014, making it very nearly Gaussian and a nearly ideally recovered map.
Figure 2 is the recovered pixon epithermal count rate map CP converted into WEH wt% (WEH(wt%) = ((20.4/Cepi − 1)/28.28)1.149 [Lawrence et al., 2006]). Here we focus on the region within 5 degrees of the south pole. Note the peak abundances of 1 wt% and greater in shadowed locales within the crater Cabaeus (C), while some other shadowed features appear to have abundances of only 0.1–0.2 wt% WEH, (110–220 ppm [H]), consistent with implanted solar wind hydrogen. These lower-H shadowed features demonstrate that the pixon reconstruction does not force higher hydrogen concentrations into the shadowed regions. Shackleton (S) appears to harbor ∼0.5 wt% WEH, Shoemaker (Sh) ∼0.2 wt%, Faustini (F) 0.3 wt%, and de Gerlache (dG) ∼0.7 wt%. If we decrease the permitted hydrogen abundance in sunlit pixels to 110 ppm, then WEH estimates go up in the permanently shadowed craters to the levels of ∼1 wt% or more derived by Feldman et al. .
5. Uncertainties and Uniqueness
 A practical way of evaluating the uncertainties is to treat the recovered map, CP, as “truth,” re-smooth it with the instrument response p, and add a randomly-generated noise realization N that is consistent with the LPNS spatial sampling and parent noise distribution. This results in a mock plausible “observed” epithermal count rate map, C*0. We then deconvolve this noisy mock map using the pixon approach in the same way as the real data were, and obtain a mock reconstruction map C*P. These steps are repeated many times with different noise realizations N in order to build up a set of mock reconstructions for which the statistical variations can be obtained. Well sampled features with high signal-to-noise ratios have small uncertainties, while others that are small or less well sampled and with lower signal-to-noise will have large uncertainties.
 We have performed 200 mock reconstructions in this way. We have propagated the uncertainty in the recovered count rates, δC*P through the equation that relates orbital epithermal count rates to WEH described earlier [Lawrence et al., 2006]. The fractional uncertainty is δw/w = 1.149 • (20.4 • δC*P/C*2P)/(20.4/C*P − 1). Figure 3 is a map of this fractional uncertainty in WEH abundance. The weight-fraction uncertainty δw/w in Faustini, Shoemaker and the unnamed crater lying nearly on the prime meridian is about 15%, while in Shackleton and de Gerlache it is about 25% and 30%, respectively. The WEH abundance uncertainties in Table 1 reflect both these reconstruction uncertainties as well as the standard deviations of the recovered WEH values within the craters.
 The 200 mock recoveries also help us understand systematically over- and underestimated values of epithermal count rate and hence WEH abundance. For example, the mean recovered value of epithermal count rate C*P in Shackleton tends to be systematically larger than the “truth” value by about 1.1 counts/sec, so that WEH estimates for the crater interior may be systematically low by about 0.1–0.2 wt%. Other features show systematic overestimates of WEH abundance. These systematic effects result from a combination of feature size, orbital sampling frequency (which largely depends on distance from the pole), and signal-to-noise ratio. In general, a small feature that is poorly sampled but is nevertheless constrained by the shadow model results in a noisy pixon fit.
 Another source of uncertainty is the permanent shadow model itself, which is poorly constrained for some features. We have varied the shadow model in another set of 200 mock reconstructions and find little systematic variation for well-defined features such as Shackleton. But large systematic variations occur in poorly defined areas such as the Cabaeus floor. In general, the WEH abundances >1 wt% are poorly constrained due to either low signal-to-noise in the original data or large sensitivity to the shadow model.
6. Discussion and Conclusions
 The previously obtained estimate of 1.5 ± 0.8 wt% WEH in permanent shadowed craters [Feldman et al., 1998, 2000, 2001] is due largely to the assumed surrounding hydrogen content of 110 ppm H in sunlit locations. Here, we permit values up to 277 ppm H in sunlight, and this effectively allows reduced concentrations of hydrogen/ice within the shadowed craters. Further, the recovered WEH abundance in polar shadowed features is inhomogeneous, suggesting that the source or loss mechanisms responsible for emplacing or removing enhanced hydrogen result in non-uniform WEH distributions. This 10- to 100-km scale inhomogeneity very probably extends to sub-feature length scales, from kilometers down to meters. Such inhomogeneity is certainly implied by the results of Crider and Vondrak , owing to the effects of impacts in redistributing volatiles.
 In locations such as Shackleton, where the recovered epithermal count rate is reasonably certain, the inferred average abundance is 0.5 wt% WEH within the permanently shadowed part of the crater. This is 0.25 wt% WEH over and above the assumed maximum of 0.25 wt% WEH in implanted solar wind hydrogen there, giving about 1.6 × 106 metric tons of water ice in the top 200 cm (the regolith gardening depth over the past ∼2 Ga). But the recovered epithermal count rate could also be explained by a linear combination of smaller, randomly distributed parcels, some with higher (“dryer”) and some with lower (“wetter”) epithermal count rates. For example, if 80% of the crater floor area has 0.25 wt% WEH due to implanted solar wind then the remaining 20% of the crater floor would have ∼3.5 wt% WEH (similar to the average results obtained by Crider and Vondrak . Such a distribution would amount to 40 km2 of ice-rich regolith, giving the equivalent of about 4.5 × 106 metric tons of water ice in the top 200 cm. The recovered epithermal count rate is also consistent with 10% of the floor area at ∼20-wt% WEH, the maximum concentration we would expect due to filling up inter-grain spaces with water ice, and the remaining floor area at 0.25 wt%. Thus it is plausible that 20 km2 of high-grade, ice-bearing regolith could be found in Shackleton alone, with 12.8 × 106 metric tons of ice in the top 200 cm. Of course, many combinations of abundance and fractional area can provide the recovered epithermal count rate in Shackleton, but the foregoing estimates bracket the limits. Just using the apparent recovered abundances in Figure 2, some 148 million metric tons of ice may exist in the upper 200 cm of regolith in permanently shadowed features poleward of 80°S, a value similar to that obtained by Feldman et al. . But if inhomogeneously distributed within craters, the inventory of near-surface polar ice could be significantly larger.
 We conclude that the results here are consistent with enhanced concentrations of hydrogenous materials in some (but not all) of the permanently shadowed cold traps. The higher abundances are greater than what is expected from implanted solar wind, and imply the presence of volatile ices. Finally, if the volatiles are inhomogeneously distributed within a permanently-shadowed locale, WEH abundances in excess of 10 wt% in limited areas are possible and consistent with both orbital neutron measurements and Earth-based radar.
 We thank the reviewers for their helpful comments. The work at Los Alamos was supported in part by NASA through Discovery Data Analysis Program grant W-7405-ENG-36, through MIPR W81EWF62288362 from the U.S. Army Corps of Engineers, and by internal Los Alamos funding, under the auspices of the U.S. Department of Energy. The work of V.R.E. and L.F.A.T. was supported by a Royal Society University Research Fellowship and a Leverhulme Research Fellowship, respectively. Work at JHU/APL was supported by NASA's Planetary Geology and Geophysics Program grant NNG06GJ13G.