Fluorescence microscopy methods are an important imaging technique in cell biology. Due to their depth sensitivity they allow a direct 3-D imaging. However, the resulting volume data sets are undersampled in depth, and the 2-D slices are blurred and noisy. Reconstructing the full 3-D information from these data is therefore a challenging task, and of high relevance for biological applications. ...

In this paper, we present a novel method for inverse filtering a two dimensional (2-D) signal using phase-based processing techniques. A 2-D sequence can be represented by a sufficient number of samples of the phase of its Fourier transform and its region of support. This is exploited to perform deconvolution. We examine the effects of additive noise and incomplete knowledge of the point spread...

We present the fourth in a series of studies devoted to the issue of improving image quality in diffuse optical tomography (DOT) by using a spatial deconvolution operation that seeks to compensate for the information-blurring property of first-order perturbation algorithms. Our earlier reports consider only static target media. Here we report spatial deconvolution applied to media with time-var...

An undersampled acquisition geometry and a limited recording aperture often produces migration noise (i.e., acquisition footprint) that blurs the subsurface reflectivity image. Here, we develop a prestack migration deconvolution (MD) filter that deblurs the migration image. The MD filter is applied to 3-D prestack SEG/EAGE salt data as well as 3-D marine data from Alaska. Results show that MD c...

Wavefield extrapolation in the (ω−x) domain provides a tool for depth migration with strong lateral variations in velocity. Implicit formulations of depth extrapolation have several advantages over explicit methods. However, the simple 3-D extension of conventional 2-D wavefield extrapolation by implicit finite-differencing requires the inversion of a 2-D convolution matrix which is computation...

We've found that Burg's two-dimensional lter ooers too much freedom in producing lateral predictions, since the predictions within a trace appear to overwhelm the lateral predictions. Instead, we x the lter coeecients along the output column so the form of the two-dimensional lter becomes equivalent to that of the FX-decon operator. The ability to control the length of this lter in time allows ...

Time-domain bidirectional deconvolution methods show great promise for overcoming the minimum-phase assumption in blind deconvolution of signals containing a mixed-phase wavelet, such as seismic data. However, usually one timedomain method is slow to converge (the slalom method) and the other one is sensitive to the initial point or preconditioner (the symmetric method). Claerbout proposed a lo...

ABSTRACT A Toeplitz-block-Toeplitz (TBT) matrix is block Toeplitz with Toeplitz blocks. TBT systems of equations arise in 2D interpolation, 2-D linear prediction and 2-D least-squares deconvolution problems. Although the doubly Toeplitz structure should be exploitable in a fast algorithm, existing fast algorithms only exploit the block Toeplitz structure, not the Toeplitz structure of the block...

Convolution and Deconvolution is having wide area of application in Digital Signal Processing. Convolution helps to estimate the output of a system with arbitrary input, with knowledge of impulse response of the system. Linear systems characteristics are completely specified by the systems impulse response, as governed by the mathematics of convolution. And with the knowledge of impulse respons...

By assuming the reflectivity series to be sparse rather than ”white”, we introduced the hybrid norm spiking deconvolution (Zhang, 2010). However one theoretical drawback of spiking deconvolution is that it assumes the source wavelet to be minimum-phase, which might not be true in practice. We propose a new formulation of spiking deconvolution with the hybrid solver that does not require such as...