# Searching for signal in a somewhat noisy landscape

I'm trying to implement a system to identify regions of high signal content in the presence of a noisy landscape. By high signal content, I simply mean intensity values significantly above background intensity values.

Intensity readings are taken at $T$ contiguous locations; at each location, $t, \text{ for } t \in [1,T]$, the intensity count, $f(t) \in [0,\infty)$, is recorded.

My current strategy is this:

Mean-correct---or, simply, subtract the mean intensity---at each observed intensity with a view to removing background noise.

1. Move a sliding window along the landscape, such that:

2. For each position $i \in [1,T]$ and window interval $w_{i,i+s-1}$:

3. compute a test statistic from the $s$ observations within the current interval, $w_{i,i+s-1}$.

4. compare this test statistic to a preselected null distribution centred on $0$.

5. compute p-value corresponding to interval $w_{i,i+s-1}$; where the p-value corresponds to the probability of committing a type I error: assuming the region characterises high-signal content when,in fact, it doesn't.

6. Implement correction for multiple testing, say Benjamini and Hochberg FDR control.

7. If two overlapping window intervals, $w_{j+s-1},w_{k+s-1}: j+s-1 \geq k$, are both within the FDR threshold, concatenate regions to form one larger region-complex.

The figure given below illustrates this concept. In this figure, two regions, say $A$ and $B$, of the given landscape are covered by the sliding window. In each region, the window is depicted at $t_{A}$ and $t_{B}$ different coverage points respectively (hence the blurring effect). I'm looking for a procedure which which will determine whether the intensity levels at $A$ and $B$ are significantly different from background. The horizontal salmon line represents the mean intensity; upon mean-correction, anything below this line will be removed.

I should also mention that I am working with several landscapes, say $L$; hence, the number of window positions---and, further hence, the number of tests---will be $\sum_{l=1}^{L}pos_{l}$, where $pos_{l}$ is the number of window positions in landscape $l$.

For this approach to work, I need to define the test statistic and corresponding null and alternative hypotheses. Given the nature of the problem, I'm not sure what form an appropriate statistic/hypotheses scenario should assume.

Could somebody provide some assistance on how to define an appropriate hypotheses scenario or perhaps suggest a more robust approach to identifying high-signal content regions?

(P.S. I'm not sure that Poisson-based approaches will work as the data seem to be over-dispersed; perhaps a negative binomial assumption would work, but I'm guessing that a non-parametric/resampling/simulation based approach might be best. Having said that, if somebody believes that a Poisson approach is appropriate, please do suggest it!)