We set the value of adaptively based on the reliability of the bounding box prediction provided by the particle filter. To this end, measure the variance of the particles and adapt the value of accordingly. A smaller variance implies a higher confidence in the estimated bounding box; thus the value of can be increased to achieve a sharper decay. If the bounding box prediction is correct, the window coefficients set equal to one correspond to the pixel locations in the foreground image that contain the foreground object.

If more than one object is present in the scene, compute a different weighting window from each of the bounding boxes. A global weighting window is then obtained as the element-wise sum of the individual windows.

The window p resulting from this procedure is related to the pixel domain representation of the signal to be recovered. Since it exploits scarcity of the signal in the wavelet domain, it need the window coefficients to be related to the wavelet domain representation of the foreground image 6. The wavelet domain window P can be computed just by applying a suitable transformation to the weighting window p. For example, the weighting window transformation is performed when a 2-D wavelet transform with two decomposition levels is adopted. The window is replicated in the seven low-resolution versions of the image in the wavelet domain. This kind of approach, even if quite simple, allows to directly compute a representation of the window P in the wavelet domain and can be applied independently of the actual window shape.

The weights necessary to solve the weighted L1 optimization problem are finally computed by taking the inverse of each coefficient of the window, so that Where the parameter e > 0 has been introduced in order to provide stability.