HI Power Spectrum Research Articles

A wide-angle formulation of foreground filters for HI intensity mapping

Neutral hydrogen intensity mapping can in principle deliver rapid and large-volume cosmological surveys with exquisitely accurate redshifts that are determined directly from imaging. However, intensity maps suffer from very strong foreground contamination. Future surveys will require efficient data pipelines to remove the foregrounds and reveal the cosmological signal. It is expected that this cleaning will not remove the signal in substantial parts of the available Fourier space and that significant loss of signal due to imperfect cleaning will be confined to specific regions of Fourier space. This suggests a strategy which is useful for simplified estimates and rapid computations — i.e., to apply foreground filters that avoid the regions where loss of signal is significant. The standard Fourier-space power spectrum and foreground filters use a flat-sky approximation and thus exclude wide-angle correlations. We provide a new geometrical formulation of foreground filters in harmonic space, which naturally includes all wide-angle effects in the power spectrum. Foreground filtering leads to a loss of isotropy in Fourier space. In harmonic space this produces off-diagonal correlations. We derive analytical expressions for the generalised HI power spectrum and its cross-power with CMB lensing, for both single-dish and interferometer mode surveys. We show numerically that the off-diagonal contributions are negligible for the auto power. In the cross power, there is a non-negligible off-diagonal contribution, but only for a small interval of the largest available scales. For auto and cross power, the signal loss due to foreground avoidance decreases with increasing multipole (i.e. smaller scales), and the loss in interferometer mode is equal to, or slightly greater than, in single-dish mode. We find that the cross power in single-dish mode vanishes below a critical multipole, ℓ < ℓ 0. For an SKA-like survey, ℓ 0 ∼ 20 – 40 over redshifts z = 1 – 3. This feature is not seen in interferometer mode as the pertinent angular scales are larger than those allowed by the minimum baseline.

The local PNG bias of neutral Hydrogen, HI

We use separate universe simulations with the IllustrisTNG galaxy formation model to predict the local PNG bias parameters bΦ and bΦδ of atomic neutral hydrogen, HI. These parameters and their relation to the linear density bias parameter b 1 play a key role in observational constraints of the local PNG parameter f NL using the HI power spectrum and bispectrum. Our results show that the popular calculation based on the universality of the halo mass function overpredicts the bΦ (b 1) and bΦδ (b 1) relations measured in the simulations. In particular, our results show that at z ≲ 1 the HI power spectrum is more sensitive to f NL compared to previously thought (bΦ is more negative), but is less sensitive at other epochs (bΦ is less positive). We discuss how this can be explained by the competition of physical effects such as that large-scale gravitational potentials with local PNG (i) accelerate the conversion of hydrogen to heavy elements by star formation, (ii) enhance the effects of baryonic feedback that eject the gas to regions more exposed to ionizing radiation, and (iii) promote the formation of denser structures that shield the HI more efficiently. Our numerical results can be used to revise existing forecast studies on f NL using 21 cm line-intensity mapping data. Despite this first step towards predictions for the local PNG bias parameters of HI, we emphasize that more work is needed to assess their sensitivity on the assumed galaxy formation physics and HI modeling strategy.

The effect of finite halo size on the clustering of neutral hydrogen

Post-reionisation 21cm intensity mapping experiments target the spectral line of neutral hydrogen (HI) resident in dark matter haloes. According to the halo model, these discrete haloes trace the continuous dark matter density field down to a certain scale, which is dependent on the halo physical size. The halo physical size defines an exclusion region which leaves imprints on the statistical properties of HI. We show how the effect of exclusion due to the finite halo size impacts the HI power spectrum, with the physical boundary of the host halo given by the splashback radius. Most importantly, we show that the white noise-like feature that appears in the zero-momentum limit of the power spectrum is exactly cancelled when the finite halo size is taken into consideration. This cancellation in fact applies to all tracers of dark matter density field, including galaxies. Furthermore, we show that the exclusion due to finite halo size leads to a sub-Poissonian noise signature on large scales, consistent with the results from N-body simulations.

High-redshift test of gravity using enhanced growth of small structures probed by the neutral hydrogen distribution

Future 21 cm intensity mapping surveys such as SKA can provide precise information on the spatial distribution of the neutral hydrogen (HI) in the post-reionization epoch. This information will allow to test the standard LCDM paradigm and with that the nature of gravity. In this work, we employ the SHYBONE simulations, which model galaxy formation in f(R) modified gravity using the IllustrisTNG model, to study the effects of modified gravity on HI abundance and power spectra. We find that the enhanced growth low-mass dark matter halos experience in f(R) gravity at high redshifts alters the HI power spectrum and can be observable through 21 cm intensity mapping. Our results suggest that the HI power spectrum is suppressed by 13\% on scales $k\lesssim2\,h\,\mathrm{Mpc}^{-1}$ at z=2 for F6, a f(R) model which passes most observational constraints. We show that this suppression can be detectable by SKA1-MID with 1000 hours of exposure time, making HI clustering a novel test of gravity at high redshift.

Impact of astrophysics on cosmology forecasts for 21 cm surveys

We use the results of previous work building a halo model formalism for the distribution of neutral hydrogen, along with experimental parameters of future radio facilities, to place forecasts on astrophysical and cosmological parameters from next generation surveys. We consider 21 cm intensity mapping surveys conducted using the BINGO, CHIME, FAST, TianLai, MeerKAT and SKA experimental configurations. We work with the 5-parameter cosmological dataset of {$\Omega_m, \sigma_8, h, n_s, \Omega_b$} assuming a flat $\Lambda$CDM model, and the astrophysical parameters {$v_{c,0}, \beta$} which represent the cutoff and slope of the HI- halo mass relation. We explore (i) quantifying the effects of the astrophysics on the recovery of the cosmological parameters, (ii) the dependence of the cosmological forecasts on the details of the astrophysical parametrization, and (iii) the improvement of the constraints on probing smaller scales in the HI power spectrum. For an SKA I MID intensity mapping survey alone, probing scales up to $\ell_{\rm max} = 1000$, we find a factor of $1.1 - 1.3$ broadening in the constraints on $\Omega_b$ and $\Omega_m$, and of $2.4 - 2.6$ on $h$, $n_s$ and $\sigma_8$, if we marginalize over astrophysical parameters without any priors. However, even the prior information coming from the present knowledge of the astrophysics largely alleviates this broadening. These findings do not change significantly on considering an extended HIHM relation, illustrating the robustness of the results to the choice of the astrophysical parametrization. Probing scales up to $\ell_{\rm max} = 2000$ improves the constraints by factors of 1.5-1.8. The forecasts improve on increasing the number of tomographic redshift bins, saturating, in many cases, with 4 - 5 redshift bins. We also forecast constraints for intensity mapping with other experiments, and draw similar conclusions.

Impact of inhomogeneous CMB heating of gas on the HI 21-cm signal during dark ages

Observations of redshifted 21-cm signal from neutral hydrogen (HI) appear to be the most promising probe of the cosmic dark ages. The signal carries information about the thermal state along with density distribution of the intergalactic medium (IGM). The cosmic microwave background radiation (CMBR), through its interaction with charged particles, plays a major role in determining the kinetic and spin temperature of HI gas in the IGM during dark ages. A Spatially fluctuating ionization fraction, which is caused by inhomogeneous recombinations, causes heat transfer from the CMBR to the IGM gas inhomogeneous. We revisit the impact of this inhomogeneous heat transfer on spatial fluctuations in the observed HI 21-cm signal over a large redshift range during dark ages. Our study shows that the effect negatively impacts fluctuations in the HI spin temperature and results in an enhanced HI 21-cm power spectrum. We find that the effect is particularly important during the transition of the gas kinetic temperature being coupled to the CMBR to fully decoupled from it, i.e., in the redshift range $30 \lesssim z \lesssim 300$. It is found that, on the average the HI power spectrum, $P_{T_b}(k, z)$ is enhanced by $\sim 4\%$, $\sim10 \%$ , $\sim 20\%$, and $\sim 30 \%$ at redshifts $60$, $90$, $140$, and $200$ respectively at $k=0.1 \, {\rm Mpc}^{-1}$. The effect becomes even more significant at lower values of $k_{\parallel}^2/k^2$ due to the reduced dominance of the peculiar velocity. It is observed that the power spectrum is enhanced by $\sim 49\%$ and $\sim 93\%$ at redshifts $140$ and $200$ respectively at $k=0.1 \, {\rm Mpc}^{-1}$ for $k_{\parallel}^2/k^2=0$. This enhancement has a weak $k$-mode dependence.

H i anisotropies associated with radio-polarimetric filaments

LOFAR detected toward 3C 196 linear polarization structures which were found subsequently to be closely correlated with cold filamentary HI structures. The derived direction-dependent HI power spectra revealed marked anisotropies for narrow ranges in velocity, sharing the orientation of the magnetic field as expected for magneto hydrodynamical turbulence. Using the Galactic portion of the Effelsberg-Bonn HI Survey we continue our study of such anisotropies in the HI distribution in direction of two WSRT fields, Horologium and Auriga; both are well known for their prominent radio-polarimetric depolarization canals. At 349 MHz the observed pattern in total intensity is insignificant but polarized intensity and polarization angle show prominent ubiquitous structures with so far unknown origin. Apodizing the HI survey data by applying a rotational symmetric 50 percent Tukey window, we derive average and position angle dependent power spectra. We fit power laws and characterize anisotropies in the power distribution. We use a Gaussian analysis to determine relative abundances for the cold and warm neutral medium. For the analyzed radio-polarimetric targets significant anisotropies are detected in the HI power spectra; their position angles are aligned to the prominent depolarization canals, initially detected by WSRT. HI anisotropies are associated with steep power spectra. Steep power spectra, associated with cold gas, are detected also in other fields. Radio-polarimetric depolarization canals are associated with filamentary HI structures that belong to the cold neutral medium (CNM). Anisotropies in the CNM are in this case linked to a steepening of the power-spectrum spectral index, indicating that phase transitions in a turbulent medium occur on all scales. Filamentary HI structures, driven by thermal instabilities, and radio-polarimetric filaments are associated with each other.

A scale-dependent bias on linear scales: the case for H i intensity mapping at z = 1

Neutral hydrogen (HI) will soon be the dark matter tracer observed over the largest volumes of Universe thanks to the 21 cm intensity mapping technique. To unveil cosmological information it is indispensable to understand the HI distribution with respect to dark matter. Using a full one-loop derivation of the power spectrum of HI, we show that higher order corrections change the amplitude and shape of the power spectrum on typical cosmological (linear) scales. These effects go beyond the expected dark matter non-linear corrections and include non-linearities in the way the HI signal traces dark matter. We show that, on linear scales at z = 1, the HI bias drops by up to 15% in both real and redshift space, which results in underpredicting the mass of the halos in which HI lies. Non-linear corrections give rise to a significant scale dependence when redshift space distortions arise, in particular on the scale range of the baryonic acoustic oscillations (BAO). There is a factor of 5 difference between the linear and full HI power spectra over the full BAO scale range, which will modify the ratios between the peaks. This effect will also be seen in other types of survey and it will be essential to take it into account in future experiments in order to match the expectations of precision cosmology.

Intensity Mapping Foreground Cleaning with Generalized Needlet Internal Linear Combination

AbstractIntensity mapping (IM) is a new observational technique to survey the large-scale structure of matter using spectral emission lines. IM observations are contaminated by instrumental noise and astrophysical foregrounds. The foregrounds are at least three orders of magnitude larger than the searched signals. In this work, we apply the Generalized Needlet Internal Linear Combination (GNILC) method to subtract radio foregrounds and to recover the cosmological HI and CO signals within the IM context. For the HI IM case, we find that GNILC can reconstruct the HI plus noise power spectra with 7.0% accuracy forz= 0.13 − 0.48 (960 − 1260 MHz) and ℓ ≲ 400, while for the CO IM case, we find that it can reconstruct the CO plus noise power spectra with 6.7% accuracy forz= 2.4 − 3.4 (26 − 34 GHz) and ℓ ≲ 3000.

Large-scale fluctuations in the cosmic ionizing background: the impact of beamed source emission

When modelling the ionisation of gas in the intergalactic medium after reionisation, it is standard practice to assume a uniform radiation background. This assumption is not always appropriate; models with radiative transfer show that large-scale ionisation rate fluctuations can have an observable impact on statistics of the Lyman-alpha forest. We extend such calculations to include beaming of sources, which has previously been neglected but which is expected to be important if quasars dominate the ionising photon budget. Beaming has two effects: first, the physical number density of ionising sources is enhanced relative to that directly observed; and second, the radiative transfer itself is altered. We calculate both effects in a hard-edged beaming model where each source has a random orientation, using an equilibrium Boltzmann hierarchy in terms of spherical harmonics. By studying the statistical properties of the resulting ionisation rate and HI density fields at redshift $z\sim 2.3$, we find that the two effects partially cancel each other; combined, they constitute a maximum $5\%$ correction to the power spectrum $P_{\mathrm{HI}}(k)$ at $k=0.04 \, h/\mathrm{Mpc}$. On very large scales ($k<0.01\, h/\mathrm{Mpc}$) the source density renormalisation dominates; it can reduce, by an order of magnitude, the contribution of ionising shot-noise to the intergalactic HI power spectrum. The effects of beaming should be considered when interpreting future observational datasets.

On the spatial distribution of neutral hydrogen in the Universe: bias and shot-noise of the H i power spectrum

The spatial distribution of neutral hydrogen (HI) in the Universe contains a wealth of cosmological information. The 21 cm emission line can be used to map the HI up to very high redshift and therefore reveal us something about the evolution of the large scale structures in the Universe. However little is known about the abundance and clustering properties of the HI over cosmic time. Motivated by this, we build an analytic framework where the relevant parameters that govern how the HI is distributed among dark matter halos can be fixed using observations. At the same time we provide tools to study the column density distribution function of the HI absorbers together with their clustering properties. Our formalism is the first one able to account for all observations at a single redshift, $z = 2.3$. The linear bias of the HI and the mean number density of HI sources, two main ingredients in the calculation of the signal-to-noise ratio of a cosmological survey, are then discussed in detail, also extrapolating the results to low and high redshift. We find that HI bias is relatively higher than the value reported in similar studies, but the shot noise level is always sub dominant, making the HI Power Spectrum always a high signal-to-noise measurements up to $z\simeq5$ in the limit of no instrumental noise and foreground contamination.

Upper Limits on the 21 cm Epoch of Reionization Power Spectrum from One Night with LOFAR

We present the first limits on the Epoch of Reionization (EoR) 21-cm HI power spectra, in the redshift range $z=7.9-10.6$, using the Low-Frequency Array (LOFAR) High-Band Antenna (HBA). In total 13\,h of data were used from observations centred on the North Celestial Pole (NCP). After subtraction of the sky model and the noise bias, we detect a non-zero $\Delta^2_{\rm I} = (56 \pm 13 {\rm mK})^2$ (1-$\sigma$) excess variance and a best 2-$\sigma$ upper limit of $\Delta^2_{\rm 21} < (79.6 {\rm mK})^2$ at $k=0.053$$h$cMpc$^{-1}$ in the range $z=$9.6-10.6. The excess variance decreases when optimizing the smoothness of the direction- and frequency-dependent gain calibration, and with increasing the completeness of the sky model. It is likely caused by (i) residual side-lobe noise on calibration baselines, (ii) leverage due to non-linear effects, (iii) noise and ionosphere-induced gain errors, or a combination thereof. Further analyses of the excess variance will be discussed in forthcoming publications.

Prospects of Detecting HI using Redshifted 21-cm Radiation at z∼3

Distribution of cold gas in the post-reionization era provides an important link between distribution of galaxies and the process of star formation. Redshifted 21 cm radiation from the Hyperfine transition of neutral Hydrogen allows us to probe the neutral component of cold gas, most of which is to be found in the interstellar medium of galaxies. Existing and upcoming radio telescopes can probe the large scale distribution of neutral Hydrogen via HI intensity mapping. In this paper we use an estimate of the HI power spectrum derived using an ansatz to compute the expected signal from the large scale HI distribution at z ~ 3. We find that the scale dependence of bias at small scales makes a significant difference to the expected signal even at large angular scales. We compare the predicted signal strength with the sensitivity of radio telescopes that can observe such radiation and calculate the observation time required for detecting neutral Hydrogen at these redshifts. We find that OWFA (Ooty Wide Field Array) offers the best possibility to detect neutral Hydrogen at z ~ 3 before the SKA (Square Kilometer Array) becomes operational. We find that the OWFA should be able to make a 3 sigma or a more significant detection in 2000 hours of observations at several angular scales. Calculations done using the Fisher matrix approach indicate that a 5 sigma detection of the binned HI power spectrum via measurement of the amplitude of the HI power spectrum is possible in 1000 hours (Sarkar, Bharadwaj and Ali, 2017).

Simulating the z = 3.35 HI 21-cm Visibility Signal for the Ooty Wide Field Array (OWFA)

The upcoming Ooty Wide Field Array (OWFA) will operate at $326.5 \, {\rm MHz}$ which corresponds to the redshifted 21-cm signal from neutral hydrogen (HI) at z = 3.35. We present two different prescriptions to simulate this signal and calculate the visibilities expected in radio-interferometric observations with OWFA. In the first method we use an input model for the expected 21-cm power spectrum to directly simulate different random realizations of the brightness temperature fluctuations and calculate the visibilities. This method, which models the HI signal entirely as a diffuse radiation, is completely oblivious to the discrete nature of the astrophysical sources which host the HI. While each discrete source subtends an angle that is much smaller than the angular resolution of OWFA, the velocity structure of the HI inside the individual sources is well within reach of OWFA's frequency resolution and this is expected to have an impact on the observed HI signal. The second prescription is based on cosmological N-body simulations. Here we identify each simulation particle with a source that hosts the HI, and we have the freedom to implement any desired line profile for the HI emission from the individual sources. Implementing a simple model for the line profile, we have generated several random realizations of the complex visibilities. Correlations between the visibilities measured at different baselines and channels provides an unique method to quantify the statistical properties of the \HI signal. We have used this to quantify the results of our simulations, and explore the relation between the expected visibility correlations and the underlying HI power spectrum.

Sky reconstruction from transit visibilities: PAON-4 and Tianlai dish array

The spherical harmonics $m$-mode decomposition is a powerful sky map reconstruction method suitable for radio interferometers operating in transit mode. It can be applied to various configurations, including dish arrays and cylinders. We describe the computation of the instrument response function, the point spread function (PSF), transfer function, the noise covariance matrix and noise power spectrum. The analysis in this paper is focused on dish arrays operating in transit mode. We show that arrays with regular spacing have more pronounced side lobes as well as structures in their noise power spectrum, compared to arrays with irregular spacing, specially in the north-south direction. A good knowledge of the noise power spectrum $C^{\mathrm{noise}}(\ell)$ is essential for intensity mapping experiments as non uniform $C^{\mathrm{noise}}(\ell)$ is a potential problem for the measurement of the HI power spectrum. Different configurations have been studied to optimise the PAON-4 and Tianlai dish array layouts. We present their expected performance and their sensitivities to the 21-cm emission of the Milky Way and local extragalactic HI clumps

Absorption variability as a probe of the multiphase interstellar media surrounding active galaxies

We examine a model for the variable free-free and neutral hydrogen absorption inferred towards the cores of some compact radio galaxies in which a spatially fluctuating medium drifts in front of the source. We relate the absorption-induced intensity fluctuations to the statistics of the underlying opacity fluctuations. We investigate models in which the absorbing medium consists of either discrete clouds or a power-law spectrum of opacity fluctuations. We examine the variability characteristics of a medium comprised of Gaussian-shaped clouds in which the neutral and ionized matter are co-located, and in which the clouds comprise spherical constant-density neutral cores enveloped by ionized sheaths. The cross-power spectrum indicates the spatial relationship between neutral and ionized matter, and distinguishes the two models, with power in the Gaussian model declining as a featureless power-law, but that in the ionized sheath model oscillating between positive and negative values. We show how comparison of the HI and free-free power spectra reveals information on the ionization and neutral fractions of the medium. The background source acts as a low-pass filter of the underlying opacity power spectrum, which limits temporal fluctuations to frequencies $\omega < \dot{\theta}_v / \theta_{\rm src}$, where $\dot{\theta}_v$ is the angular drift speed of the matter in front of the source, and it quenches the observability of opacity structures on scales smaller than the source size $\theta_{\rm src}$. For drift speeds of $\sim 10^3\,$km s$^{-1}$ and source brightness temperatures $\sim 10^{12}\,$K, this limitation confines temporal opacity fluctuations to timescales of order several months to decades.

Modelling the post-reionization neutral hydrogen (H i ) bias

Observations of the neutral Hydrogen (\HI ) 21-cm signal hold the potential of allowing us to map out the cosmological large scale structures (LSS) across the entire post-reionization era ($z \leq 6$). Several experiments are planned to map the LSS over a large range of redshifts and angular scales, many of these targeting the Baryon Acoustic Oscillations. It is important to model the \HI distribution in order to correctly predict the expected signal, and more so to correctly interpret the results after the signal is detected. In this paper we have carried out semi-numerical simulations to model the \HI distribution and study the \HI power spectrum $P_{\HI}(k,z)$ across the redshift range $1 \le z \le 6$. We have modelled the \HI bias as a complex quantity $\tilde{b}(k,z)$ whose modulus squared $b^2(k,z)$ relates $P_{\HI}(k,z)$ to the matter power spectrum $P(k,z)$, and whose real part $b_r(k,z)$ quantifies the cross-correlation between the \HI and the matter distribution. We study the $z$ and $k$ dependence of the bias, and present polynomial fits which can be used to predict the bias across $0 \le z \le6$ and $0.01 \le k \le 10 \, {\rm Mpc}^{-1}$. We also present results for the stochasticity $r=b_r/b$ which is important for cross-correlation studies.

The effects of the small-scale DM power on the cosmological neutral hydrogen (HI) distribution at high redshifts

The particle nature of dark matter remains a mystery. In this paper, we consider two dark matter models—Late Forming Dark Matter (LFDM) and Ultra-Light Axion (ULA) models—where the matter power spectra show novel effects on small scales. The high redshift universe offers a powerful probe of their parameters. In particular, we study two cosmological observables: the neutral hydrogen (HI) redshifted 21-cm signal from the epoch of reionization, and the evolution of the collapsed fraction of HI in the redshift range 2 < z < 5. We model the theoretical predictions of the models using CDM-like N-body simulations with modified initial conditions, and generate reionization fields using an excursion set model. The N-body approximation is valid on the length and halo mass scales studied. We show that LFDM and ULA models predict an increase in the HI power spectrum from the epoch of reionization by a factor between 2–10 for a range of scales 0.1 < k < 4 Mpc−1. Assuming a fiducial model where a neutral hydrogen fraction x̄HI = 0.5 must be achieved by z = 8, the reionization process allows us to put approximate bounds on the redshift of dark matter formation zf > 4 × 105 (for LFDM) and the axion mass ma > 2.6 × 10−23 eV (for ULA). The comparison of the collapsed mass fraction inferred from damped Lyman-α observations to the theoretical predictions of our models lead to the weaker bounds: zf > 2 × 105 and ma > 10−23 eV. These bounds are consistent with other constraints in the literature using different observables; we briefly discuss how these bounds compare with possible constraints from the observation of luminosity function of galaxies at high redshifts. In the case of ULAs, these constraints are also consistent with a solution to the cusp-core problem of CDM.

Nonlinear modulation of the HI power spectrum on ultra-large scales. I

Intensity mapping of the neutral hydrogen brightness temperature promises to provide a three-dimensional view of the universe on very large scales. Nonlinear effects are typically thought to alter only the small-scale power, but we show how they may bias the extraction of cosmological information contained in the power spectrum on ultra-large scales. For linear perturbations to remain valid on large scales, we need to renormalize perturbations at higher order. In the case of intensity mapping, the second-order contribution to clustering from weak lensing dominates the nonlinear contribution at high redshift. Renormalization modifies the mean brightness temperature and therefore the evolution bias. It also introduces a term that mimics white noise. These effects may influence forecasting analysis on ultra-large scales.

Extracting H i cosmological signal with generalized needlet internal linear combination

HI intensity mapping is a new observational technique to map fluctuations in the large-scale structure of matter using the 21 cm emission line of atomic hydrogen (HI). Sensitive radio surveys have the potential to detect Baryon Acoustic Oscillations (BAO) at low redshifts (z < 1) in order to constrain the properties of dark energy. Observations of the HI signal will be contaminated by instrumental noise and, more significantly, by astrophysical foregrounds, such as Galactic synchrotron emission, which is at least four orders of magnitude brighter than the HI signal. Foreground cleaning is recognised as one of the key challenges for future radio astronomy surveys. We study the ability of the Generalized Needlet Internal Linear Combination (GNILC) method to subtract radio foregrounds and to recover the cosmological HI signal for a general HI intensity mapping experiment. The GNILC method is a new technique that uses both frequency and spatial information to separate the components of the observed data. Our results show that the method is robust to the complexity of the foregrounds. For simulated radio observations including HI emission, Galactic synchrotron, Galactic free-free, radio sources and 0.05 mK thermal noise, we find that we can reconstruct the HI power spectrum for multipoles 30 < l < 150 with 6% accuracy on 50% of the sky for a redshift z ~ 0.25.