Use of the domina.on property for interval valued digital signal - PowerPoint PPT Presentation

Use of the domina.on property for interval valued digital signal processing O. Strauss

W HAT IS LINEAR FILTERING ? x(t) y(t) Imprecise signal processing x k y n κ (t) y n = Σ x k κ n-k y(t) = (x ★ κ )(t) k κ is the impulse response of the filter κ summative kernel : Σ κ n = 1 n 2

F IND THE IMPULSE RESPONSE F IND THE IMPULSE RESPONSE … CAN HAVE A DRASTIC INFLUENCE ON THE PROCESSED SIGNAL … Imprecise signal processing W E PROPOSE A WAY TO INDUCE A KIND OF ROBUSTNESS IN SIGNAL PROCESSING BY REPRESENTING THE CONVEX HULL OF ALL OUTPUTS OF A WHOLE SET OF COHERENT FILTERS . … AND SOMETIMES IT CAN BE DIFFICULT TO SPECIFY THE 3 RIGHT IMPULSE RESPONSE !

D IFFERENT WAYS TO EXPRESS CONVOLUTION  y n = Σ x k κ n-k k Imprecise signal processing  y n = Σ x k κ n κ n is the kernel κ translated in n k k  y n = E {x} P is the probability of being in the κ n P κ n neighborhood of n (via κ ) … thus a set of kernel is equivalent to a set of probabiltity … i.e. a credal set. 4

Imprecise signal processing 5 P RACTICAL REPRESENTATION

H ANDLING EPISTEMIC UNCERTAINTY Imprecise signal processing H OW TO REPRESENT WHAT HAPPEN TO A RANDOM VARIABLE WHEN IT GOES THROUGH AN ILL ‐ KNOWN SYSTEM ? 6

D ISCUSSION T HANK YOU FOR YOUR ATTENTION Imprecise signal processing • How to combine in a single model epistemic uncertainty and random varia.ons (due to observa.on)? • How to keep low‐computa.onal complexity? • How to provide results that can be easily interpretable? • How to access to informa.on of this par.al knowledge? • How to compare the new methods we propose to more 7 tradi.onal methods (especially when comparing bipolar to unipolar or interval‐valued to single valued)?