On homomorphic deconvolution of bandpass signals

A convolution may be represented as x(.)=r(.)* w(.). The goal of deconvolution is to extract r(.) and w(.) from a knowledge of x(.) and it finds numerous applications in digital signal processing. Of practical interest in oil exploration is the case where w(.) is a seismic pressure wavelet, x(.) is the observed seismic response, and r(.) is the reflectivity of the Earth. A number of procedures have been proposed, including predictive, deterministic, and homomorphic deconvolution. Homomorphic deconvolution has been found to be particularly efficient for those cases where x(.) is known to be fullband. This paper presents a robust constructive procedure for efficient homomorphic deconvolution for those cases where x(.) is a bandpass signal. Extensive comparisons with other methods for deconvolving bandpass signals on measured seismic data traces (including the Novaya Zemlya event) illustrate the improvement in the deconvolution     

Maximum-Likelihood Seismic Deconvolution

The purpose of this paper is to describe a broad spectrum of seismic deconvolution problems and solutions which we refer to collectively as maximum-likelihood (seismic) deconvolution (MLD). Our objective is to perform deconvolution and wavelet estimation for the case of nonminimum phase wavelets. Our approach is to exploit state-variable technology, maximum-likelihood estimation, and a sparse spike train (Bernoulli-Gaussian) model for the reflection signal. Our solution requires detection of significant reflectors, wavelet and variance identification (nonlinear optimization), and estimation of the spike density parameter.     

Optimal seismic deconvolution: distributed algorithms

Deconvolution is one of the most important aspects of seismic signal processing. The objective of the deconvolution procedure is to remove the obscuring effect of the wavelet's replica making up the seismic trace and therefore obtain an estimate of the reflection coefficient sequence. This paper introduces a new deconvolution algorithm. Optimal distributed estimators and smoothers are utilized in the proposed solution. The new distributed methodology, perfectly suitable for a multisensor environment, such as the seismic signal processing, is compared to the centralized approach, with respect to computational complexity and architectural efficiency. It is shown that the distributed approach greatly outperforms the currently used centralized methodology offering flexibility in the design of the data fusion network     

改进的超分辨率图像重建算法

针对超分辨率卷积神经网络(SRCNN)卷积层较少、训练时间长、不易收敛且表达和泛化能力受限等问题,提出了一种残差反卷积SRCNN(RD-SRCNN)算法.首先利用不同大小的卷积核进行卷积操作,以更好地提取低分辨率图像中的细节特征;然后将获取的图像特征输入由不同大小卷积核构成的卷积层和指数线性单元激活层组成的残差网络,并...     

Simultaneous wavelet estimation and deconvolution of reflectionseismic signals

The problem of simultaneous wavelet estimation and deconvolution is investigated with a Bayesian approach under the assumption that the reflectivity obeys a Bernoulli-Gaussian distribution. Unknown quantities, including the seismic wavelet, the reflection sequence, and the statistical parameters of reflection sequence and noise are all treated as realizations of random variables endowed with suitable prior distributions. Instead of deterministic procedures that can be quite computationally burdensome, a simple Monte Carlo method, called Gibbs sampler, is employed to produce random samples iteratively from the joint posterior distribution of the unknowns. Modifications are made in the Gibbs sampler to overcome the ambiguity problems inherent in seismic deconvolution. Simple averages of the random samples are used to approximate the minimum mean-squared error (MMSE) estimates of the unknowns. Numerical examples are given to demonstrate the performance of the method     

Principle phase decomposition: a new concept in blind seismic deconvolution

This paper outlines an exciting new approach for carrying out blind seismic deconvolution. In this algorithm, overlapping source wavelets are modeled as amplitude-modulated sinusoids, and blind deconvolution is carried out by initially determining the seismogram's principle phase components. Once the principle phases are determined, a Rao-Blackwellized particle filter (RBPF) is utilized to separate the corresponding overlapping source wavelets. This deconvolution technique is referred to as principle phase decomposition (PPD). The PPD technique makes use of the fact that in reflection seismology the discrete convolution operation can be represented as the summation of several source wavelets of differing arrival times. In this algorithm, a jump Markov linear Gaussian system (JMLGS) is defined where changes (jumps) in the state-space system and measurement equations are due to the occurrences and losses of overlapping source wavelet events. The RBPF obtains optimal estimates of the possible overlapping source wavelets by individually weighting and subsequently summing a bank of Kalman filters (KFs). These KFs are specified and updated by samples drawn from a Markov chain distribution that defines the probability of the overlapping source wavelets that compose the JMLGS. In addition, hidden Markov model filters are utilized for refining the principle phase estimates.     

On the LTI properties of adaptive feedforward systems with tapdelay-line regressors

It is shown that an adaptive system whose regressor is formed by tap delay-line (TDL) filtering of a multitone sinusoidal signal is representable as a parallel connection of a linear time-invariant (LTI) block and a linear time-varying (LTV) block. A norm-bound (induced 2-norm) is computed explicitly on the LTV block and is shown to decrease as N^-1, where N is the number of taps. Hence, the adaptive system becomes LTI in the limit as the number of taps goes to infinity. In the more realistic case where the number of taps N is finite, the new “LTI plus norm-bounded perturbation” representation renders, for the first time, the adaptive system analyzable by standard robust control methods     

Adaptive blind source separation of multiple-input multiple-output linearly time-varying FIR system

A new adaptive blind separation scheme for sources mixed by a multiple-input multiple-output (MIMO) linearly time-varying (LTV) FIR system is proposed. First, by dividing measured samples into a series of short segments, time-varying coefficients of the mixing system are approximated by polynomials in time over each segment. Then, a two-step BSS scheme is presented for the approximated system. The first step is to estimate the time variation and convolution effects of the mixing system, and reduce the LTV-FIR mixing system to a linearly time-invariant (LTI) instantaneous system using the conventional input/output system identification scheme. The second step uses the mutual independence knowledge of the sources to further separate the sources from the LTI instantaneous system. The theoretical and experimental studies show that the new BSS scheme has an improved performance in separating sources mixed by an LTV-FIR system.     

Multiscale deconvolution of sensor array signals viasum-of-cumulants

This correspondence presents a solution to a multiscale deconvolution problem using higher order spectra where the data to be deconvolved consist of noise-corrupted sensor array measurements. We assume that the data are generated as a convolution of an unknown wavelet with reflectivity sequences that are linearly time-scaled versions of an unknown reference reflectivity sequence. This type of data occurs in many signal processing applications, including sonar and seismic processing. Our approach relies on exploiting the redundancy in the measurements due to time scaling and does not require knowledge of the wavelet or the reflectivity sequences. We formulate and solve the deconvolution problem as a quadratic minimization subject to a quadratic constraint in the sum-of-cumulants (SOC) domain. The formulation using the SOC approach reduces the effect of additive Gaussian noise on the accuracy of the results when compared with the standard time-domain formulation. We demonstrate this improvement using a simulation example     

An algorithm for successive identification of reflections

A new algorithm for successive identification of seismic reflections is proposed. Generally, the algorithm can be viewed as a curve matching method for images with specific structure. However, in the paper, the algorithm works on seismic signals assembled to constitute an image in which the investigated reflections produce curves. In numerical examples, the authors work on signals assembled in CMP gathers. The key idea of the algorithm is to estimate the reflection curve parameters and the reflection coefficients along these curves by combining the multipulse technique and the generalized Radon transform. The multipulse technique is used for wavelet identification in each trace, and the generalized Radon transform is used to coordinate the wavelet identification between the individual traces. Furthermore, a stop criterion and a reflection validation procedure are presented. The stop criterion stops the reflection estimation when the actual estimated reflection is insignificant. The reflection validation procedure ensures that the estimated reflections follow the shape of the investigated reflection curves. The algorithm is successfully used in two numerical examples. One is based on a synthetic CMP gather, whereas the other is based on a real recorded CMP gather. Initially, the algorithm requires an estimate of the wavelet that can be performed by any wavelet estimation method.     

On the Application of the Fast Kalman Algorithm to Adaptive Deconvolution of Seismic Data

The application of a recently proposed fast implementation of the recursive least squares algorithm, called the Fast Kalman Algorithm (FKA) to adaptive deconvolution of seismic data is discussed. The newly proposed algorithm does not require the storage and updating of a matrix to calculate the filter gain, and hence is computationally very efficient. Furthermore, it has an interesting structure yielding both the forward and backward prediction residuals of the seismic trace and thus permits the estimation of a ?smoothed residual? without any additional computations. The paper also compares the new algorithm with the conventional Kalman algorithm (CKA) proposed earlier [3] for seismic deconvolution. Results of experiments on simulated as well as real data show that while the FKA is a little more sensitive to the choice of some initial parameters which need to be selected carefully, it can yield comparable performance with greatly reduced computational effort.     

Minimum-Variance and Maximum-Likelihood Deconvolution for Noncausal Channel Models

This paper extends the previous works of Mendel and his students on the subject of deconvolution from causal channel (wavelet) models to noncausal channel models. Noncausal wavelets occur, for example, in seismic data processing when a land vibrator is used to excite the Earth. Minimum-variance and maximum-likelihood deconvolution algorithms are developed herein for symmetrical and/or nonsymmetrical time-invariant wavelets that are excited by stationary and/or nonstationary white noise inputs. Minimum-variance deconvolution algorithms for a noncausal wavelet turn out to be quite different than those for a causal wavelet; however, maximum-likelihood deconvolution algorithms for a noncausal wavelet, which involve event detection and amplitude restoration, are essentially the same as those for a causal wavelet. Examples are provided that illustrate the performance of the different deconvolution algorithms.     

An EM algorithm for wavelet-based image restoration

This paper introduces an expectation-maximization (EM) algorithm for image restoration (deconvolution) based on a penalized likelihood formulated in the wavelet domain. Regularization is achieved by promoting a reconstruction with low-complexity, expressed in the wavelet coefficients, taking advantage of the well known sparsity of wavelet representations. Previous works have investigated wavelet-based restoration but, except for certain special cases, the resulting criteria are solved approximately or require demanding optimization methods. The EM algorithm herein proposed combines the efficient image representation offered by the discrete wavelet transform (DWT) with the diagonalization of the convolution operator obtained in the Fourier domain. Thus, it is a general-purpose approach to wavelet-based image restoration with computational complexity comparable to that of standard wavelet denoising schemes or of frequency domain deconvolution methods. The algorithm alternates between an E-step based on the fast Fourier transform (FFT) and a DWT-based M-step, resulting in an efficient iterative process requiring O(NlogN) operations per iteration. The convergence behavior of the algorithm is investigated, and it is shown that under mild conditions the algorithm converges to a globally optimal restoration. Moreover, our new approach performs competitively with, in some cases better than, the best existing methods in benchmark tests.     

卷积型小波包变换及其快速算法

经典的小波包变换会使分解序列的长度递减,这在某些领域并不是很有利。为了解决这一问题,本文提出了卷积型小波包变换算法,利用这种变换,不管信号被小波包分解多少层,分解得到的各频道序列长度始终与原始信号一致。文中推导了卷积型小波包的正变换和逆变换的快速算法,并以对一个实际信号的处理为例,与经典的小波包分析结果进行了比较,它们的效果是一致的,但是卷积型小波包却免去了重构这一过程的手续。     

The application of blind channel identification techniques toprestack seismic deconvolution

One objective of seismic signal processing is to identify the layered subsurface structure by sending seismic wavelets into the ground. This is a blind deconvolution process since the seismic wavelets are usually not measurable and therefore, the subsurface face layers are identified only by the reflected seismic signals. Conventional methods often approach this problem by making assumptions about the subsurface structures and/or the seismic wavelets. In this paper an alternative technique is presented. It applies blind channel identification methods to prestack seismic deconvolution. A unique feature of this proposed method is that no such assumptions are needed. In addition, it fits into the structure of current seismic data acquisition techniques, thus no extra cost is involved. Simulations on both synthetic and field seismic data demonstrate that it is a promising new method for seismic signal processing     

Wavelet-based inverse halftoning for error diffused halftones

This paper describes a technique for inverse halftoning based on the wavelet domain deconvolution that comprises Fourier-domain followed by wavelet-domain noise suppression, in order to benefit from the advantages of each of them. The proposed algorithm can be formulated as a linear deconvolution problem. In fact, we model such a gray-scale image to be the result of a convolution of the original image with a point spread function (PSF) and a colored noise. Our method performs inverse halftoning by first inverting the model specified convolution operator and then attenuating the residual noise using scalar wavelet-domain shrinkage. Using simulations, we verify that the proposed method is competitive with state-of-the-art inverse halftoning techniques in the mean-square-sense and that has also good visual performance. We illustrate the results with simulations on some examples.     

A new normalized relatively stable lattice structure

This paper proposes a new lattice filter structure that has the following properties. When the filter is linear time invariant (LTI), it is equivalent to the celebrated Gray-Markel lattice. When the lattice parameters vary with time, it sustains arbitrary rates of time variations without sacrificing a prescribed degree of stability, provided that the lattice coefficients are magnitude bounded in a region where all LTI lattices have the same degree of stability. We also show that the resulting LTV lattice obeys an energy contraction condition. This structure thus generalizes the normalized Gray-Markel lattice, which has similar properties but only with respect to stability as opposed to relative stability     

基于FPGA的YOLOv5s网络高效卷积加速器设计

为提升在资源受限情况下的嵌入式平台上卷积神经网络(Convolutional Neural Network, CNN)目标识别的资源利用率和能效,提出了一种适用于YOLOv5s目标识别网络的现场可编程门阵列(Field Programmable Gate Array, FPGA)共享计算单元的并行卷积加速结构,该结构通过共享3×3卷积和1×1卷积的计算单元提高了加速器硬件资源利用率。此外,还利用卷积层BN(Batch Normalization)层融合、模型量化、循环分块以及双缓冲等策略,提高系统计算效率并减少硬件资源开销。实验结果表明,加速器在200 MHz的工作频率下,实现的卷积计算峰值性能可达97.7 GOPS(Giga Operations per Second),其YOLOv5s网络的平均计算性可达78.34 GOPS,与其他FPGA加速器方案相比在DSP效率、能耗比以及整体性能等方面具有一定的提升。     

On the mobile‐to‐mobile linear time‐variant shallow‐water acoustic channel response

We expose some concepts concerning the channel impulse response (CIR) of linear time‐varying (LTV) channels to give a proper characterization of the mobile‐to‐mobile underwater channel. We find different connections between the linear time‐invariant (LTI) CIR of the static channel and 2 definitions of LTV CIRs of the dynamic mobile‐to‐mobile channel. These connections are useful to design a dynamic channel simulator from the static channel models available in the literature. Such feature is particularly interesting for overspread channels, which are hard to characterize by a measuring campaign. Specifically, the shallow water acoustic (SWA) channel is potentially overspread because of the signal low velocity of propagation, which prompts long delay spread responses and great Doppler effect. Furthermore, from these connections between the LTI static CIRs and the LTV dynamic CIRs, we find that the SWA mobile‐to‐mobile CIR does not only depend on the relative speed between transceivers, but also on the absolute speed of each of them referred to the velocity of propagation. Nevertheless, publications about this topic do not consider it and formulate their equations in terms of the relative speed between transceivers. We illustrate our find using 2 couples of examples where, even though the relative speed between the mobiles is the same, their CIRs are not.