Abstract We consider multichannel deconvolution in a periodic setting with long-memory errors under three different scenarios for the convolution operators, i.e., super-smooth, regular-smooth and box-car convolutions. We investigate global performances of linear and hard-thresholded non-linear wavelet estimators for functions over a wide range of Besov spaces and for a variety of loss functions defining the risk. In particular, we obtain upper bounds on convergence rates using the L p -risk ( 1 ≤ p ∞ ) . Contrary to the case where the errors follow independent Brownian motions, it is demonstrated that multichannel deconvolution with errors that follow independent fractional Brownian motions with different Hurst parameters results in a much more involved situation. An extensive finite-sample numerical study is performed to supplement the theoretical findings.
A deconvolution technique for deriving more resolved signals from lidar signals with typical CO2 laser pulses is proposed, utilizing special matrices constructed from the temporal profile of laser pulses. It is shown that near-range signals can be corrected and small-scale variations of backscattered signals can be retrieved with this technique. Deconvolution errors as a result of noise in lidar data and in the laser pulse profile are also investigated numerically by computer simulation. A main application of lidar remote sensing is to provide spatial resolved data. Based on the fundamental relationship between space and time the distance can be calculated from the photons’ time of flight. Accordingly, the distance resolution is limited by the time resolution of the lidar detector. Furthermore, if the system response function of the lidar is longer than the time resolution interval of the detector, the measured lidar signal is smeared, and the effective distance resolution decreases. In theory, this loss of resolution can be corrected by deconvolution of the measured signal with the system response function. Measured lidar signals are superposed by noise which makes a direct deconvolution impossible because of the effect of noise amplification. In this paper, a technique is presented which allows for a stable deconvolution of lidar signal returns without any filtering in the frequency domain. It is based on the Richardson-Lucy algorithm for image reconstruction. Simulations of short distance lidar signals have been used to compare the method with conventional deconvolution algorithms such as the Fourier transformation.