A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal

Unveiling meaningful geophysical information from seismic data requires to deal with both random and structured "noises". As their amplitude may be greater than signals of interest (primaries), additional prior information is especially important in performing efficient signal separation. We address here the problem of multiple reflections, caused by wave-field bouncing between layers. Since only approximate models of these phenomena are available, we propose a flexible framework for time-varying adaptive filtering of seismic signals, using sparse representations, based on inaccurate templates. We recast the joint estimation of adaptive filters and primaries in a new convex variational formulation. This approach allows us to incorporate plausible knowledge about noise statistics, data sparsity and slow filter variation in parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a constrained minimization problem that alleviates standard regularization issues in finding hyperparameters. The approach demonstrates significantly good performance in low signal-to-noise ratio conditions, both for simulated and real field seismic data

Blind deconvolution of medical ultrasound images: parametric inverse filtering approach

©2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.DOI: 10.1109/TIP.2007.910179The problem of reconstruction of ultrasound images by means of blind deconvolution has long been recognized as one of the central problems in medical ultrasound imaging. In this paper, this problem is addressed via proposing a blind deconvolution method which is innovative in several ways. In particular, the method is based on parametric inverse filtering, whose parameters are optimized using two-stage processing. At the first stage, some partial information on the point spread function is recovered. Subsequently, this information is used to explicitly constrain the spectral shape of the inverse filter. From this perspective, the proposed methodology can be viewed as a ldquohybridizationrdquo of two standard strategies in blind deconvolution, which are based on either concurrent or successive estimation of the point spread function and the image of interest. Moreover, evidence is provided that the ldquohybridrdquo approach can outperform the standard ones in a number of important practical cases. Additionally, the present study introduces a different approach to parameterizing the inverse filter. Specifically, we propose to model the inverse transfer function as a member of a principal shift-invariant subspace. It is shown that such a parameterization results in considerably more stable reconstructions as compared to standard parameterization methods. Finally, it is shown how the inverse filters designed in this way can be used to deconvolve the images in a nonblind manner so as to further improve their quality. The usefulness and practicability of all the introduced innovations are proven in a series of both in silico and in vivo experiments. Finally, it is shown that the proposed deconvolution algorithms are capable of improving the resolution of ultrasound images by factors of 2.24 or 6.52 (as judged by the autocorrelation criterion) depending on the type of regularization method used

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference

Discrete pdf estimation in the presence of noise

The problem of estimating a pdf from measurements has been widely studied by many researchers. However, most of the work was focused on estimating a probability density function of continuous random variables, especially in the absence of noise. In this paper, we consider a model for representing discrete probability density functions based on multirate dsp models. Using this model, we propose an efficient and stable scheme for pdf estimation when the measurements are corrupted by independent additive noise. This approach makes use of well-known results from multirate dsp theory, especially that of biorthogonal partners. Simulation results are given, which clearly show the advantage of the proposed method

Image restoration using regularized inverse filtering and adaptive threshold wavelet denoising

Although the Wiener filtering is the optimal tradeoff of inverse filtering and noise smoothing, in the case when the blurring filter is singular, the Wiener filtering actually amplify the noise. This suggests that a denoising step is needed to remove the amplified noise .Wavelet-based denoising scheme provides a natural technique for this purpose .<br />In this paper a new image restoration scheme is proposed, the scheme contains two separate steps : Fourier-domain inverse filtering and wavelet-domain image denoising. The first stage is Wiener filtering of the input image , the filtered image is inputted to adaptive threshold wavelet denoising stage . The choice of the threshold estimation is carried out by analyzing the statistical parameters of the wavelet sub band coefficients like standard deviation, arithmetic mean and geometrical mean . The noisy image is first decomposed into many levels to obtain different frequency bands. Then soft thresholding method is used to remove the noisy coefficients, by fixing the optimum thresholding value by this method .Experimental results on test image by using this method show that this method yields significantly superior image quality and better Peak Signal to Noise Ratio (PSNR). Here, to prove the efficiency of this method in image restoration , we have compared this with various restoration methods like Wiener filter alone and inverse filter

Višekanalna slijepa dekonvolucija slike zasnovana na inovacijama

The linear mixture model (LMM) has recently been used for multi-channel representation of a blurred image. This enables use of multivariate data analysis methods such as independent component analysis (ICA) to solve blind image deconvolution as an instantaneous blind source separation (BSS) requiring no a priori knowledge about the size and origin of the blurring kernel. However, there remains a serious weakness of this approach: statistical dependence between hidden variables in the LMM. The contribution of this paper is an application of the ICA algorithms to the innovations of the LMM to learn the unknown basis matrix. The hidden source image is recovered by applying pseudo-inverse of the learnt basis matrix to the original LMM. The success of this approach is due to the property of the innovations of being more independent and more non-Gaussian than original processes. Our good, consistent simulation and experimental results demonstrate viability of the proposed concept.Linearni model miješanja (LMM) se u posljednje vrijeme koristi i za višekanalnu reprezentaciju zamućene slike. Na taj se način multivarijantne metode analize podataka, poput analize nezavisnih komponenata (ICA), mogu iskoristiti i za rješavanje slijepe dekonvolucije slike bezmemorijskom slijepom separacijom izvora (BSS), a koja ne zahtjeva a priori znanje o veličini i podrijetlu jezgre zamućenja. Ipak, postoji velik nedostatak ovog pristupa: statistička zavisnost između skrivenih varijabli LMM-a. Doprinos ovog rada je primjena ICA algoritama na inovacijama LMM-a u postupku učenja nepoznate bazne matrice. Skrivene izvorne slike se restauriraju primjenom pseudo-inverza naučene bazne matrice na originalni LMM. Uspjeh predloženog pristupa se može zahvaliti svojstvu inovacija da su više nezavisne i više ne-gausovske od originalnog procesa. Dobri i konzistentni rezultati naših simulacija i eksperimenata demonstriraju upotrebljivost predloženog koncepta