It depends on the 'object' you are trying to identify inside noise.

If your hidden object is a function, then you have two strategies to resolve the problem:

1)You adopt a proper model and do regression and statistical tests for the results

2)You use methods that do not imply any kind of known functional form, but instead of it they use the definition of the hidden property (for example: the inflection point).

These methods are divided again in two distinct disciplines:

i. those that are based on a proper orthogonal projection

ii. those that are based on geometrical aspects and build consistent estimators of them.

An example of identifying the inflection point by using strategy 2)ii. you can find here:

https://www.researchgate.net/publication/229066111_A_simple_and_numerical_stable_algorithm_for_solving_the_cone_projectionproblem_based_on_a_Gram-Schmidt_process?ev=prf_pub

Perhaps you should be more specific: what exactly do you want to identify?

Article A simple and numerical stable algorithm for solving the cone...

Thank you Demetris,

I agree, there are algorithms for finding objects using known properties; and there are algorithms for determining properties of known objects. It seems your 2ii is of the second type. Would it be able to find an inflection point if you do not know where is the line?

By the mentioned 2ii methods it is possible now to find two consistent estimators of the inflection point by using only the (xi,yi) data available from laboratory. If the inflection point does not exist (because data is strictly convex or concave for example), the methods will estimate the upper or lower edge of the xi-interval. Otherwise, they will give you at the worst case scenario an interval where this point exists. For the best case they will give you two intervals including it.

When you are asking about the line, do you mean that you are not able to pick-up the appropriate (xi,yi) data set?

Can you give me an example?

Thank you Demetris,

This is exactly the reason for the difficulty: data in 2D cover all (xi,yi) and the line points are not brighter than noise points. Most existing algorithms require considering many possibilities, leading to exponential complexity. Two examples are in

Perlovsky, L.I. & Ilin, R. (2012). Mathematical Model of Grounded Symbols: Perceptual Symbol System. Journal of Behavioral and Brain Science, 2, 195-220; doi:10.4236/jbbs.2012.22024; http://www.scirp.org/journal/jbbs/

more examples are in

Perlovsky, L.I., Deming R.W., & Ilin, R. (2011). Emotional Cognitive Neural Algorithms with Engineering Applications. Dynamic Logic: from vague to crisp. Springer, Heidelberg, Germany.

And I would always like to find out about other approaches.

I understood. My point to your research can be probably a very fast sub-algorithm for the recognition of sigmoid or convex/concave patterns inside the 2-D chaos.

And one more suggestion: in order to scan properly the 2-D area of interest it is necessary to define a proper norm of 'order', perhaps a measure of entropy or something else. Then when you are scanning by your software algorithm you can fix the areas with 'smiles" for example. Finally you can adopt any algorithm like the above 2ii or other, in order to identify the hidden object. Good luck!

One interesting strategy will be analyzing the signal’s moments. Even if the target has the same mean that the clutter, it’s possible to distinguish them by analyzing the statistical variations. For example, two range cells may have the same mean but completely difference variances.