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one of the most serious challenges in the hunt for transiting extrasolar planets is the removal of the various systematics remaining in the photometric databases even after employing sophisticated methods of ccd image reduction . sometimes called as `` red noise ''
@xcite , systematics / trends may show up in many ways .
their most common appearance is a drift with @xmath0  d@xmath1 frequency due to variations of the point - spread function and numerous other parameters , for example focus change , sub - pixel coordinate drifts , etc .
in addition to these most trivial systematics , we may have many others , from transients ( e.g. , imperfect removal of cosmic rays ) to periodic saturation of bright stars , depending on moon phase . during the past several years
it has been realized that , except for the simple , high signal - to - noise ratio cases , filtering out these systematics from the databases is absolutely crucial from the point of view of transit search .
therefore , efforts have been taken to devise post processing algorithms that are capable of whitening out the data from the systematics .
there are two methods in this field that attracted wider interest .
the method sysrem by @xcite uses basically an iterative principal component analysis to filter out the most prominent systematics from the data . the trend filtering algorithm ( tfa ) by @xcite is a least - squares method that is capable of filtering out nearly arbitrary systematics , assuming that the selected set of templates is `` flavorous '' enough , i.e. , it contains the light curves necessary for the approximation of the type of trend observed in the target .
here we present tests on the signal recovery capability of tfa .
for completeness , we briefly summarize the basic steps of tfa .
first we select a _
template set _ of @xmath2 light curves from the photometric database of the field of interest . from these \{@xmath3 } time series ( sampled in @xmath4 moments of time )
, we construct the following filter : @xmath5 the coefficients \{@xmath6 } for a target \{@xmath7 } are determined by minimizing the following expression : @xmath8 ^ 2 \hskip 2 mm .\end{aligned}\ ] ] here the function @xmath9 is derived in the following way : @xmath10[r]{(3)}\ ] ] namely , in the case of period search we assume that the observed signal is dominated by systematics and noise , and therefore , the filter is expected to yield minimum dispersion around the constant signal average @xmath11 .
once the signal is identified , we can recover its shape by iteratively approximating the noiseless and trend - free signal \{@xmath9}. ( the iteration is indicated by the symbol @xmath12 in eq .  ( 3 ) . ) in this iterative process we assume that \{@xmath9 } can be represented by a low - parameter model , and that the observed signal minus the systematics yield the true signal with white noise .
the datasets used in this paper are listed in table  1 .
we test transit detection efficiency ( tde ) , false alarm probability ( fap ) and signal reconstruction capability ( src ) .
for testing src on datasets different from those of hatnet @xcite , we use the hat - p-1 @xcite observations by the 60/90/180 cm schmidt telescope of the konkoly observatory .    to show that tfa is capable of filtering out nearly all systematics , we compute the distribution function of the peak frequencies obtained by the bls analysis @xcite . the result of this analysis for field # 125
is shown in fig .  1 .
we see that the original data includes many stars with various periodic systematics , some of which are not too easy to relate to the daily change of the observational conditions . for example , the strongest peak at @xmath13  d@xmath1 is most probably associated with the saturation of the bright stars , because after omitting the first @xmath14 stars , the peak at this frequency becomes less prominent than the ones corresponding to other systematics .
lrrrrl set & @xmath4 & @xmath15 & @xmath16[d ] & i [ mag ] & purpose + hatnet # 125 & @xmath17 & @xmath18 & @xmath19 & @xmath20 & tde , fap + hatnet # 127 & @xmath21 & @xmath22 & @xmath23 & @xmath24 & fap + hatnet # 148 & @xmath25 & @xmath26 & @xmath27 & @xmath28 & src + hat - p-1 , schmidt & @xmath29 & @xmath30 & @xmath31 & @xmath32 & src +    , width=226 ]    , width=226 ]    we have already demonstrated in kovcs et al .
( 2005 ) the ability of tfa of detecting shallow transits that are buried in noise and systematics .
because the statistics we use have slightly changed from then , here we show the results of tests conducted with the new statistics .
we inject a periodic transit signal in the given target from the first @xmath33 stars of field # 125 .
then we run a tfa / bls analysis on the target and check if the dsp parameter @xcite corresponding to the highest peak in the frequency spectrum exceeds a given limit .
the dsp parameter expresses the significance of the dip corresponding to the transit derived from the analysis . in order to exclude binaries with light reflection and gravitational effects
, dsp also includes weighting by the most significant fourier component of the out - of - transit variation .
when computing dsp , we always use the tfa code in the signal reconstruction mode to get a better estimate on this parameter .
properties of the injected signal and the number of detections are listed in table  2 .
we note that the synthetic signal has a flat out - of - transit part and a trapeze shape with rather long ingress / egress durations .
the condition of detection is given by a cutoff imposed on dsp .
the value of this cutoff is large enough to eliminate false alarms ( see sect .  4 ) .
we see that there is a highly significant increase in the detection probability due to the application of tfa .
this increase is especially striking when the top 500 bright stars are tested .
these are the ones that are most seriously affected by systematics related to saturation effects ( see above ) .
we note that the detection ratio can be slightly increased ( from @xmath34% to @xmath35% ) if we choose templates only from this brighter set of stars .
crrc tfa & @xmath15 & @xmath36 & @xmath36[% ] + 0 & @xmath33 & @xmath37 & @xmath38 + 1 & @xmath33 & @xmath39 & @xmath40 + 0 & @xmath41 & @xmath42 & @xmath43 + 1 & @xmath41 & @xmath44 & @xmath34 +
by `` false alarms '' we mean those cases when the detection statistics indicate the presence of a signal , but the probability distribution of the statistics ( derived on pure noise ) shows that the observed value may also occur due to a random event and the probability of this to happen is `` greater than we would like to '' . in assessing fap we resort to direct statistical tests , in which we generate pure gaussian time series on the time base of the observed light curves .
we analyze these artificial time series and count the number of cases when dsp exceeds a prescribed limit . in this way we get estimates on faps for a given dataset when
tfa and bls are used .
the results of the tests are presented in table  3 .
several conclusions can be drawn from this table .
first of all , as expected , application of tfa introduces correlation in the time series .
this increases fap by a substantial amount .
second , larger number of data points results in a decrease of fap .
third , larger number of templates leads to stronger correlation , and therefore , to an increase of fap .
fourth , although increasing the number of data points decreases fap , it is present in a relative high value even for higher dsp cutoff values ( when we already expect a visible sign of the ( fake ) transit in the folded / binned light curve .    in an attempt to reduce fap , the following method is suggested . by using several tfa runs , corresponding to various template numbers , we compute dsp values for the given database . due to the way the template sets are constructed ,
these results are expected to be largely independent from each other . in a conservative approach of signal detection
, we require the signal to be present in all these runs . in the primary selection of transit candidates we require only that the dip is negative ( i.e. , corresponding to dimming ) and that @xmath45 .
the result of this multiple template fap filtering is shown in the lower three lines of table  3 .
we see that the method is very effective already with three different tfa runs . for example , even for the sparsely sampled field # 127 , with three or more different tfa runs we can filter out false alarms with a probability better than 99.9% for signals with dsp@xmath46 .
lrrrcrrr & & & + @xmath47  : & 5 & 6 & 7 & & 5 & 6 & 7 + @xmath48 & 68 & 7 & 0 & & 26 & 3 & 1 + a & 827 & 400 & 107 & & 258 & 24 & 2 + b & 856 & 523 & 168 & & 306 & 31 & 6 + c & 842 & 560 & 220 & & 394 & 42 & 3 + d & 890 & 638 & 328 & & 474 & 60 & 5 + ab & 386 & 112 & 9 & & 73 & 2 & 0 + abc & 184 & 38 & 1 & & 25 & 0 & 0 + abcd & 97 & 21 & 1 & & 14 & 0 & 0 +
signal reconstruction is an essential ( but optional ) part of signal processing when tfa is used .
this is because we do not know _ a priori _ which part of the observed signal comes from the systematics and which one from the true signal ( and all these are coupled with noise ) . without knowing the signal parameters _ a priori _ , we resort to an iterative scheme in reconstructing the true signal ( see also sect .  2 ) .
our experiments on the hatnet database show that this reconstruction can be quite successful without making any assumption on the signal shape .
once the signal shape is reliably identified , one can proceed by more specific assumptions , e.g. , by using trapeze transit shapes , and thereby further decreasing the number of parameters fitted . to illustrate the efficiency of the tfa reconstruction , we show two examples in fig .  2 .    ] , signal - to - noise ratio ( snr ) of the bls spectrum , dsp , snr of the out - of - transit variation and its peak frequency in the units of the bls frequency . on the right we have : star i d , average magnitude , plotting frequency [ d@xmath1 ] , number of data points , dsp .
the reconstruction of hat - p-1 was made without using its nearby companion star ads16402 a. in both cases no assumptions were made on the signal shape .
[ tfarec],width=245 ]    ] , signal - to - noise ratio ( snr ) of the bls spectrum , dsp , snr of the out - of - transit variation and its peak frequency in the units of the bls frequency . on the right
we have : star i d , average magnitude , plotting frequency [ d@xmath1 ] , number of data points , dsp .
the reconstruction of hat - p-1 was made without using its nearby companion star ads16402 a. in both cases no assumptions were made on the signal shape .
[ tfarec],width=207 ]
filtering out systematics from astrophysical time series is nearly mandatory if a survey - type analysis is made with the goal of reaching the theoretical white noise limit of signal detection . in the search for extrasolar transiting planets
this issue becomes even more highlighted due to the delicacy of the detection .
we have shown in this paper that tfa is capable of filtering out various systematics , thereby allowing the detection and a concomitant reconstruction of faint regular ( e.g. , simple- or multi - periodic ) signals .
furthermore , by requiring multiple detections in time series filtered by various tfa templates , false alarm probability can be pushed down near to the white noise limit .
support for program number hst - hf-01170.01-a to g.   .
b.  was provided by nasa through a hubble fellowship grant from the space telescope science institute .
operation of the hatnet project is funded in part by nasa grant nng04gn74 g .
we also acknowledge otka k-60750 .
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we present additional tests of our algorithm aimed at filtering out systematics due to data reduction and instrumental imperfections in time series obtained by ensemble photometry . signal detection efficiency is demonstrated , and a method of decreasing the false alarm probability is presented . including the recently discovered transiting extrasolar planet hat - p-1 , we show various examples on the signal reconstruction capability of the method .