We present telescoping recursive representations for both continuous and discrete indexed noncausal Gauss-Markov random fields. Our recursions start at the boundary (for example, a hypersurface in R, d ≥ 1) and telescope inwards. Under appropriate conditions, the recursions for the random field are differential/difference representations driven by white noise, for which we can use standard recu...

We introduce a recursive algorithm for performing compressed sensing on streaming data. The approach consists of a) recursive encoding, where we sample the input stream via overlapping windowing and make use of the previous measurement in obtaining the next one, and b) recursive decoding, where the signal estimate from the previous window is utilized in order to achieve faster convergence in an...

Estimation problems with bounded, uniformly distributed noise arise naturally in reconstruction problems from over complete linear expansions with subtractive dithered quantization. We present a simple recursive algorithm for such bounded-noise estimation problems. The mean-square error (MSE) of the algorithm is “almost” (1 ), where is the number of samples. This rate is faster than the (1 ) MS...

Parameter selection for the criterion weighting matrix is concerned based on the information of both modifying the past estimation residuals and renewing the present estimation residual error . After minimizing the system estimation error, an optimal recursive algorithm is given. In this method the system data record can be used efficiently. The consistency of the new recursive algorithm is ana...

Adaptive systems rely on recursive estimation of a firmly bounded complexity. As a rule, they have to use an approximation of the posterior probability density function (pdf), which comprises unreduced information about the estimated parameter. In recursive setting, the latest approximate pdf is updated using the learnt system model and the newest data and then approximated. The fact that appro...