*C. Foreground Recovering*

The objective of the foreground recovery module is to reconstruct the foreground image ft starting from its quantized random projections ftp . This can be done exploiting temporal correlation by means of a linear transformation. Given a joint measurement matrix Д and a 3-D wavelet transformation matrix y , it can be solve the following optimization problem,

stacking G column vectors representing the projections of the foreground images.

Leveraging the results about weighted L1 optimization is proposing an alternative approach to exploit temporal correlation. Rather than striving for a sparser representation of the signal, this can be attempt to enhance the reconstruction performance inferring information about the current foreground image from the previous one and using such information to compute the weights that might help solving the recovery problem. To be more precise, an estimate of the foreground image is computed as ft = Ф 0 , being 0 the solution of the following optimization problem:

minimize\W0\ s.t. “ftp – АФ0 <s (6)

II Ш t 2

Where W is a diagonal matrix with the weights w = ^ w(1)…w(Non the diagonal, Ф is an orthonormal 2-D wavelet transformation matrix and e=FTft is the vector representing ft in the wavelet domain.