This paper presents an image adaptive linear filtering method for the reconstruction of the RGB (red, blue, green) color coordinates of a pixel from the lossy compressed luminance/chrominance color coordinates. In the absence of quantization noise, the RGB coordinates of a pixel can be perfectly reconstructed by employing a standard, fixed filter whose support includes only the luminance/chromi...

This paper studies the problem of digital signal reconstruction in the multirate framework. In contrast to the typical digital domain formulation in the current digital signal processing, we present a solution that optimizes an analog performance, via the modern sampled-data control. While the standard technique often indicates that an ideal digital low-pass filter is preferred, we show that th...

This paper proposes an optimization procedure of a spatial filter in a water level detection system. The water level of running water of a river is detected by applying a temporal filter and a spatial filter to a video of various river scenery. Previously, we have proposed an algorithm based on “addition” of frames and “horizontal” detection of edges. We have confirmed its superiority to the ex...

We discuss the solution of numerically ill-posed overdetermined systems of equations using Tikhonov a-priori-based regularization. When the noise distribution on the measured data is available to appropriately weight the fidelity term, and the regularization is assumed to be weighted by inverse covariance information on the model parameters, the underlying cost functional becomes a random varia...

We present an algorithm based on numerical techniques that have become standard for solving nonlinear integral equations: Newton's method, homotopy continuation, the multilevel and random projection to solve inversion problem appears when retrieving electric field of ultrashort laser pulse from a two-dimensional intensity map measured with frequency-resolved optical gating (FROG), dispersion-sc...

A wavelet transform algorithm combined with a conjugate gradient method is used for the inversion of Poisson’s integral (downward continuation), used in airborne gravimetry applications. The wavelet approximation is dependent on orthogonal wavelet base functions. The integrals are approximated in finite multiresolution analysis subspaces. Mallat’s algorithm is used in the multiresolution analys...

An inverse hydrologic optics problem is solved using a recent intrinsic regularization scheme coupled to a standard Ant Colony System (ACS). The regularization scheme pre-selects candidate solutions based on their smoothness, quantified by a Tikhonov norm. The Chlorophyll profile is reconstructed from radiance experimental measurements in the ocean water for several depths and single wavelength...

We study the regularising properties of Tikhonov regularisation on the sequence space l with weighted, non-quadratic penalty term acting separately on the coefficients of a given sequence. We derive sufficient conditions for the penalty term that guarantee the well-posedness of the method, and investigate to which extent the same conditions are also necessary. A particular interest of this pape...