Reconstruction and subgaussian operator

Candes, Romberg and Tao recently studied problems of approximate and exact reconstruction of sparse signals from incomplete random measurements and related them to the eigenvalue behavior of submatrices of matrices of random measurements. In particular they introduced the notion they called the 'uniform uncertainty principle' (UUP) and studied it for Gaussian, Bernoulli and Fourier ensembles. We shall introduce a different--geometric--approach to approximate and exact reconstruction problem which yields to a more general setting for all subgaussian random measurements.