Quantitative Acoustic Microscopy (QAM) is an imaging technology utilising high frequency ultrasound to produce quantitative two-dimensional (2D) maps of acoustical and mechanical properties of biological tissue at microscopy scale. Increased frequency QAM allows for finer resolution at the expense of increased acquisition times and data storage cost. Compressive sampling (CS) methods have been employed to produce QAM images from a reduced sample set, with recent state of the art utilising Approximate Message Passing (AMP) methods. In this paper we investigate the use of AMP-Net, a deep unfolded model for AMP, for the CS reconstruction of QAM parametric maps. Results indicate that AMP-Net can offer superior reconstruction performance even in its stock configuration trained on natural imagery (up to 63% in terms of PSNR), while avoiding the emergence of sampling pattern related artefacts.

Ultrasound Localization Microscopy (ULM) offers great advances compared to conventional ultrasound imaging, enabling the reconstruction of microvascular structures with micrometer-scale precision. Most model-based localization approaches for ULM rely on a sequential five-step framework, which complicates parameter tuning and results in intricate tissue filtering. In addition, insufficient consideration of point spread function (PSF) also affects the final results. End-to-end data-driven solutions offer promising results yet require training data and ground-truths. In this study, we introduced a novel approach, based on computational super-resolution referred to as BSRPCA - Blind Super-Resolved Robust Principal Component Analysis, to address these challenges. Our method replaces the first three steps of the ULM process with a single super-resolution step. Experimental results on both in silico and in vivo datasets have proven the effectiveness of our method compared to the other benchmarks.

This letter addresses the problem of single image super resolution using Plug-and-play (PnP) frameworks incorporating with residual learning. We pro pose a novel PnP algorithm, PlaSo, which integrates residual learning mechanisms into diffusion processes to mitigate common challenges such as hallucination artifacts and over-smoothing. Furthermore, by initializing the reverse sampling process from the degraded input rather than random noise, PlaSo achieves faster con vergence. Experiments demonstrate that PlaSo consis tently outperforms state-of-the-art methods, both qual itatively and quantitatively. Our code is available at: https://gitlab.irit.fr/minds/theseeric/plaso.

This letter presents a novel quantum algorithm for signal denoising, which performs a thresholding in the frequency domain through amplitude amplification and using an adaptive threshold determined by local mean values. The proposed algorithm is able to process both classical and quantum signals. It is parametrically faster than previous classical and quantum denoising algorithms. Numerical results show that it is efficient at removing noise of both classical and quantum origin, significantly outperforming existing quantum algorithms in this respect, especially in the presence of quantum noise.

Denoising is omnipresent in image processing. It is usually addressed with algorithms relying on a set of hyperparameters that control the quality of the recovered image. Manual tuning of those parameters can be a daunting task, which calls for the development of automatic tuning methods. Given a denoising algorithm, the best set of parameters is the one that minimizes the error between denoised and ground-truth images. Clearly, this ideal approach is unrealistic, as the ground-truth images are unknown in practice. In this work, we propose unsupervised cost functions — i.e., that only require the noisy image — together with reach this ideal gold standard performance. Specifically, the proposed approach makes it possible to obtain an average PSNR output within less than 1% of the best achievable PSNR

In this paper, we propose a blueprint of a new deep network unfolding a baseline quantum mechanics-based adaptive denoising scheme (De-QuIP). Relying on the theory of quantum many-body physics, the De-QuIP architecture incorporates local patch similarity measures through a term akin to interaction in quantum physics. Our proposed deep network embeds both quantum interactions and other quantum concepts, mainly the Hamiltonian operator. The integration of these quantum tools brings a nonlocal structure to the proposed deep network that harnesses the power of the convolutional layers to enhance the adaptability of the model. Thus, recasting De-QuIP in the framework of a deep learning network while preserving the essence of the baseline structure is the main contribution of this work. Experiments conducted on the Gaussian denoising problem, chosen here for illustration purpose, over a large sample set demonstrate start-of-the-art performance of the proposed deep network, dubbed as Deep-De-QuIP hereafter. Based on the properties of De-QuIP, its intrinsic adaptive structure, Deep-De-QuIP network could be easily extended to other noise models.

Sparse representation of real-life images is a very effective approach in imaging applications, such as denoising. In recent years, with the growth of computing power, data-driven strategies exploiting the redundancy within patches extracted from one or several images to increase sparsity have become more prominent. This paper presents a novel image denoising algorithm exploiting such an image-dependent basis inspired by the quantum many-body theory. Based on patch analysis, the similarity measures in a local image neighborhood are formalized through a term akin to interaction in quantum mechanics that can efficiently preserve the local structures of real images. The versatile nature of this adaptive basis extends the scope of its application to image-independent or image-dependent noise scenarios without any adjustment. We carry out a rigorous comparison with contemporary methods to demonstrate the denoising capability of the proposed algorithm regardless of the image characteristics, noise statistics and intensity. We illustrate the properties of the hyperparameters and their respective effects on the denoising performance, together with automated rules of selecting their values close to the optimal one in experimental setups with ground truth not available. Finally, we show the ability of our approach to deal with practical images denoising problems such as medical ultrasound image despeckling applications.

Recent advances in deep learning led to several algorithms for the accurate diagnosis of pneumonia from chest X-rays. However, these models require large training medical datasets, which are sparse, isolated, and generally private. Furthermore, these models in medical imaging are known to over-fit to a particular data domain source, i.e., these algorithms do not conserve the same accuracy when tested on a dataset from another medical center, mainly due to image distribution discrepancies. In this work, a domain adaptation and classification technique is proposed to overcome the over-fit challenges on a small dataset. This method uses a private-small dataset (target domain), a public-large labeled dataset from another medical center (source domain), and consists of three steps. First, it performs a data selection of the source domain's most representative images based on similarity constraints through principal component analysis subspaces. Second, the selected samples from the source domain are fit to the target distribution through an image to image translation based on a cycle-generative adversarial network. Finally, the target train dataset and the adapted images from the source dataset are used within a convolutional neural network to explore different settings to adjust the layers and perform the classification of the target test dataset. It is shown that fine-tuning a few specific layers together with the selected-adapted images increases the sorting accuracy while reducing the trainable parameters. The proposed approach achieved a notable increase in the target dataset's overall classification accuracy, reaching up to 97.78 % compared to 90.03 % by standard transfer learning.

Decomposing an image through Fourier, DCT or wavelet transforms is still a common approach in digital image processing, in number of applications such as denoising. In this context, data-driven dictionaries and in particular exploiting the redundancy withing patches extracted from one or several images allowed important improvements. This paper proposes an original idea of constructing such an image-dependent basis inspired by the principles of quantum many-body physics. The similarity between two image patches is introduced in the formalism through a term akin to interaction terms in quantum mechanics. The main contribution of the paper is thus to introduce this original way of exploiting quantum many-body ideas in image processing, which opens interesting perspectives in image denoising. The potential of the proposed adaptive decomposition is illustrated through image denoising in presence of additive white Gaussian noise, but the method can be used for other types of noise such as image-dependent noise as well. Finally, the results show that our method achieves comparable or slightly better results than existing approaches.

Aircraft certification procedures require the estimation of wing deformation, which is a very challenging problem in photogrammetry applications. Indeed, in real flight conditions with varying environment, 3D reconstruction is strongly degraded. To cope with this issue, we propose to introduce prior knowledge about the wing mechanical limits in the photogrammetry reconstruction method. These mechanical limits are expressed as appropriate regularizations that are included into the classical bundle adjustment step. The proposed approach is evaluated using data acquired on a real aircraft yielding promising results.

This paper introduces a novel algorithm for the fusion of magnetic resonance and ultrasound images, based on a patch-wise polynomial model relating the gray levels of the two imaging systems (called modalities). Starting from observation models adapted to each modality and exploiting a patch-wise polynomial model, the fusion problem is expressed as the minimization of a cost function including two data fidelity terms and two regularizations. This minimization is performed using a PALM-based algorithm, given its ability to handle nonlinear and possibly non-convex functions. The efficiency of the proposed method is evaluated on phantom data. The resulting fused image is shown to contain complementary information from both magnetic resonance (MR) and ultrasound (US) images, i.e., with a good contrast (as for the MR image) and a good spatial resolution (as for the US image).

This paper introduces a new fusion method for magnetic resonance (MR) and ultrasound (US) images, which aims at combining the advantages of each modality, i.e., good contrast and signal to noise ratio for the MR image and good spatial resolution for the US image. The proposed algorithm is based on two inverse problems, performing a super-resolution of the MR image and a denoising of the US image. A polynomial function is introduced to model the relationships between the gray levels of the two modalities. The resulting inverse problem is solved using a proximal alternating linearized minimization framework. The accuracy and the interest of the fusion algorithm are shown quantitatively and qualitatively via evaluations on synthetic and experimental phantom data.

A volumetric non-blind single image super-resolution technique using tensor factorization has been recently introduced by our group. That method allowed a 2-order-of-magnitude faster high-resolution image reconstruction with equivalent image quality compared to state-of-the-art algorithms. In this work a joint alternating recovery of the high-resolution image and of the unknown point spread function parameters is proposed. The method is evaluated on dental computed tomography images. The algorithm was compared to an existing 3D super-resolution method using low-rank and total variation regularization, combined with the same alternating PSF-optimization. The two algorithms have shown similar improvement in PSNR, but our method converged roughly 40 times faster, under 6 minutes both in simulation and on experimental dental computed tomography data.

Joint deconvolution and segmentation of ultrasound images is a challenging problem in medical imaging. By adopting a hierarchical Bayesian model, we propose an accelerated Markov chain Monte Carlo scheme where the tissue reflectivity function is sampled thanks to a recently introduced proximal unadjusted Langevin algorithm. This new approach is combined with a forward-backward step and a preconditioning strategy to accelerate the convergence, and with a method based on the majorization-minimization principle to solve the inner nonconvex minimization problems. As demonstrated in numerical experiments conducted on both simulated and in vivo ultrasound images, the proposed method provides high-quality restoration and segmentation results and is up to six times faster than an existing Hamiltonian Monte Carlo method.

Available super-resolution techniques for 3-D images are either computationally inefficient prior-knowledge-based iterative techniques or deep learning methods which require a large database of known low-resolution and high-resolution image pairs. A recently introduced tensor-factorization-based approach offers a fast solution without the use of known image pairs or strict prior assumptions. In this paper, this factorization framework is investigated for single image resolution enhancement with an offline estimate of the system point spread function. The technique is applied to 3-D cone beam computed tomography for dental image resolution enhancement. To demonstrate the efficiency of our method, it is compared to a recent state-of-the-art iterative technique using low-rank and total variation regularizations. In contrast to this comparative technique, the proposed reconstruction technique gives a 2-order-of-magnitude improvement in running time-2 min compared to 2 h for a dental volume of 282×266×392 voxels. Furthermore, it also offers slightly improved quantitative results (peak signal-to-noise ratio and segmentation quality). Another advantage of the presented technique is the low number of hyperparameters. As demonstrated in this paper, the framework is not sensitive to small changes in its parameters, proposing an ease of use.

Most of the existing ultrasound image restoration methods consider a spatially-invariant point-spread function (PSF) model and circulant boundary conditions. While computationally efficient, this model is not realistic and severely limits the quality of reconstructed images. In this work, we address ultrasound image restoration under the hypothesis of piece-wise linear vertical variation of the PSF based on a small number of prototypes. No assumption is made on the structure of the prototype PSFs. To regularize the solution, we use the classical elastic net constraint. Existing methodologies are rendered impractical either due to their reliance on matrix inversion or due to their inability to exploit the strong convexity of the objective. Therefore, we propose an optimization algorithm based on the Accelerated Composite Gradient Method, adapted and optimized for this task. Our method is guaranteed to converge at a linear rate and is able to adaptively estimate unknown problem parameters. We support our theoretical results with simulation examples.

The main scope of this paper is to show how tools from quantum mechanics, in particular the Schroedinger equation, can be used to construct an adaptive transform suitable for signal and image processing applications. The proposed dictionary is obtained by considering the signal or image as a discrete potential in Schroedinger equation, further used to construct the Hamiltonien operator. In order to illustrate its practical interest in signal and image processing, we provide denoising results in the case of signal-dependent noise, which is the noise type the most adapted to the proposed approach.

Existing ultrasound deconvolution approaches unrealistically assume, primarily for computational reasons, that the convolution model relies on a spatially invariant kernel and circulant boundary conditions. We discard both restrictions and introduce an image formation model applicable to ultrasound imaging and deconvolution based on an axially varying kernel, which accounts for arbitrary boundary conditions. Our model has the same computational complexity as the one employing spatially invariant convolution and has negligible memory requirements. To accommodate the state-of-the-art deconvolution approaches when applied to a variety of inverse problem formulations, we also provide an equally efficient adjoint expression for our model. Simulation results confirm the tractability of our model for the deconvolution of large images. Moreover, in terms of accuracy metrics, the quality of reconstruction using our model is superior to that obtained using spatially invariant convolution.

Fetal activity parameters such as movements, fetal heart rate (FHR) and the associated parameters are essential indicators of the fetal well being, and thus, their monitoring is of high importance. Many existing monitoring systems provide partial monitoring information. For instance, most of the systems perform estimation and analysis of FHR. However, this is not enough compared to the biophysical profile or Manning test which is known to be a reference, but time consuming and not very flexible. We developed a multiple-sensor Doppler system to investigate Maning-like test. This system provides a huge amount of data which are processed in order to access the fetal activity parameters. We show here a synthesis of the main results in terms of classification.

Compressive deconvolution, combining compressive sampling and image deconvolution, represents an interesting possibility to reconstruct enhanced ultrasound images from compressed measurements. The model of compressive deconvolution includes, in addition to the measurement matrix, a 2D convolution operator carrying the information on the system point spread function which is usually unkown in practice. In this paper, we propose a novel alternating minimization-based optimization scheme to invert the resulting linear model, to jointly reconstruct enhanced ultrasound images and estimate the point spread function. The performance of the method is evaluated on both Shepp-Logan phantom and simulated ultrasound data.

This paper studies a new three-step procedure for detecting anomalies in crop development using temporal indicators derived from multispectral satellite images. These anomalies may result from seeding problems, heterogeneity, deficiency and stress. The first step estimates different biophysical and statistical parameters associated with these parameters from the observed images. In a second step, missing data that arise from the existence of clouds or limited coverage in the satellite image are reconstructed. Finally, the mean shift algorithm is used as an unsupervised classifier to detect anomalies in these reconstructed data. The proposed procedure is evaluated using agronomic indicators estimated from SPOT 5 Take 5 satellite images from the Beauce area in France.

Approximate Message Passing (AMP) is an iterative reconstruction algorithm that performs signal denoising within a compressive sensing framework. We propose the use of heavy tailed distribution based image denoising, specifically using a Cauchy prior based Maximum A-Posteriori (MAP) estimate within a wavelet based AMP compressive sensing structure. The use of this MAP denoising algorithm provides extremely fast convergence for image based compressive sensing. The proposed method converges approximately twice as fast as the compared AMP methods whilst providing superior final MSE results over a range of measurement rates.

This paper proposes a joint segmentation and deconvolution Bayesian method for medical ultrasound (US) images. Contrary to piecewise homogeneous images, US images exhibit heavy characteristic speckle patterns correlated with the tissue structures. The generalized Gaussian distribution (GGD) has been shown to be one of the most relevant distributions for characterizing the speckle in US images. Thus, we propose a GGD-Potts model defined by a label map coupling US image segmentation and deconvolution. The Bayesian estimators of the unknown model parameters, including the US image, the label map, and all the hyperparameters are difficult to be expressed in a closed form. Thus, we investigate a Gibbs sampler to generate samples distributed according to the posterior of interest. These generated samples are finally used to compute the Bayesian estimators of the unknown parameters. The performance of the proposed Bayesian model is compared with the existing approaches via several experiments conducted on realistic synthetic data and in vivo US images.

This paper addresses the problem of single image super-resolution (SR), which consists of recovering a high-resolution image from its blurred, decimated, and noisy version. The existing algorithms for single image SR use different strategies to handle the decimation and blurring operators. In addition to the traditional first-order gradient methods, recent techniques investigate splitting-based methods dividing the SR problem into up-sampling and deconvolution steps that can be easily solved. Instead of following this splitting strategy, we propose to deal with the decimation and blurring operators simultaneously by taking advantage of their particular properties in the frequency domain, leading to a new fast SR approach. Specifically, an analytical solution is derived and implemented efficiently for the Gaussian prior or any other regularization that can be formulated into an l2 -regularized quadratic model, i.e., an l2 - l2 optimization problem. The flexibility of the proposed SR scheme is shown through the use of various priors/regularizations, ranging from generic image priors to learning-based approaches. In the case of non-Gaussian priors, we show how the analytical solution derived from the Gaussian case can be embedded into traditional splitting frameworks, allowing the computation cost of existing algorithms to be decreased significantly. Simulation results conducted on several images with different priors illustrate the effectiveness of our fast SR approach compared with existing techniques.

The interest of compressive sampling in ultrasound imaging has been recently extensively evaluated by several research teams. Following the different application setups, it has been shown that the RF data may be reconstructed from a small number of measurements and/or using a reduced number of ultrasound pulse emissions. Nevertheless, RF image spatial resolution, contrast and signal to noise ratio are affected by the limited bandwidth of the imaging transducer and the physical phenomenon related to US wave propagation. To overcome these limitations, several deconvolution-based image processing techniques have been proposed to enhance the ultrasound images. In this paper, we propose a novel framework, named compressive deconvolution, that reconstructs enhanced RF images from compressed measurements. Exploiting an unified formulation of the direct acquisition model, combining random projections and 2D convolution with a spatially invariant point spread function, the benefit of our approach is the joint data volume reduction and image quality improvement. The proposed optimization method, based on the Alternating Direction Method of Multipliers, is evaluated on both simulated and in vivo data.

This paper introduces a new technique for compressive sampling reconstruction of biomedical ultrasound images that exploits two types of prior information. On the one hand, our proposed approach is based on the observation that ultrasound RF echoes are best characterised statistically using alpha-stable distributions. On the other hand, through knowledge of the acquisition process, the support of the RF echoes in the Fourier domain can be easily inferred. Together, these two facts inform an iteratively reweighted least squares (IRLS) algorithm, which is shown to outperform previously proposed reconstruction techniques, both visually and in terms of two objective evaluation measures.

This paper addresses the problem of ultrasound image restoration within a Bayesian framework. The distribution of the ultrasound image is assumed to be a generalized Gaussian distribution (GGD). The main contribution of this work is to propose a hierarchical Bayesian model for estimating the GGD parameters. The Bayesian estimators associated with this model are difficult to be expressed in closed form. Thus we investigate a Markov chain Monte Carlo method which is used to generate samples asymptotically distributed according to the posterior of interest. These generated samples are finally used to compute the Bayesian estimators of the GGD parameters. The performance of the proposed Bayesian model is tested with synthetic data and compared with the performance obtained with the expectation maximization algorithm.

Quantification of regional myocardial motion and deformation from cardiac ultrasound is fostering considerable research efforts. Despite the tremendous improvements done in the field, all existing approaches still face a common limitation which is intrinsically connected with the formation of the ultrasound images. Specifically, the reduced lateral resolution and the absence of phase information in the lateral direction highly limit the accuracy in the computation of lateral displacements. In this context, this paper introduces a novel setup for the estimation of cardiac motion with ultrasound. The framework includes an unconventional beamforming technique and a dedicated motion estimation algorithm. The beamformer aims at introducing phase information in the lateral direction by producing transverse oscillations. The estimator directly exploits the phase information in the two directions by decomposing the image into two 2-D single-orthant analytic signals. An in silico evaluation of the proposed framework is presented on five ultra-realistic simulated echocardiographic sequences, where the proposed motion estimator is contrasted against other two phase-based solutions exploiting the presence of transverse oscillations and against block-matching on standard images. An implementation of the new beamforming strategy on a research ultrasound platform is also shown along with a preliminary in vivo evaluation on one healthy subject.

In the field of ultrasound imaging, resolution enhancement is an up-to-date challenging task. Many device-based approaches have been proposed to overcome the low resolution nature of ultrasound images but very few works deal with post-processing methods. This paper investigates a novel approach based on semi-blind deconvolution formulation and alternating direction method framework in order to perform the ultrasound image restoration task. The algorithm performance is addressed using optical images and synthetic ultrasound data for a various range of criteria. The results demonstrate that our technique is more robust to uncertainties in the a priori ultrasonic pulse than classical non-blind deconvolution methods.

This paper deals with multifractal characterization of skin cancer in ultrasound images. The proposed method establishes a multifractal analysis framework of such images based on a new multiresolution indicator, called the maximum wavelet coefficient, derived from the wavelet leaders. Two main contributions are brought up: first, it proposes a method for the estimation of multifractal features. Second, it reveals the potential of multifractal features to characterize skin melanoma. In order to study the efficiency of our maximum coefficient estimator, we compare its results on a simulated image against wavelet leaders based estimator. We then apply the approach on various samples from different skin images. Results show that the extracted features make a promising quantitative indicator to distinguish between different tissues.

We showed that multidimensional parametric modeling is an interesting method to improve the spatial resolution of ultrasound images. The major issue is to estimate simultaneously the model parameters and orders. We recently proposed a least-square-based technique which is able to estimate both orders and parameters of a general N-dimensional auto-regressive (AR) model. This method has been extended to an instrumental variable-like approach accounting for the characteristics of ultrasound images. The proposed method is based on specific factorization of the regression matrix. The methodology developed may be applied to an AR model of any dimension (3 or 4D). However, we focus here on the 2D situation and show improvement of resolution of ultrasound images by this method.

We showed in a previous study that the detection of micro-emboli can be markedly improved by taking into account the quasi-cyclostationary properties of the blood Doppler signal. However, in order to detect still smaller events, we propose to combine the use of synchronous detectors and sub-band decomposition. We evaluated and compared the detector's performance to existing methods by using both numerical modeling of the Doppler signal and ROC curves.

In a previous study we have shown that take into account the quasi-cyclostationary properties of the blood Doppler signal is useful to detect embolus (red blood cell aggregates). In this latter approach, we have first considered a simple "off-line" synchronous detector. As results were very interesting, we have thought that the correlation spectrum could be an interesting alternative to the synchronous detection. As the correlation spectrum of in vivo signal seems to be too complicated, we propose here to elucidate this apparent complexity by analytically computing the correlation spectrum of Doppler signal model with or without embolus

This paper presents a technique for accessing multidimensional complex number AR model order and parameters through matrix factorization. The principle of this technique consists of the transformation of the multidimensional model to a pseudo SISO (simple input simple output) AR model then performing factorization of the covariance matrix of the data. This factorization then leads to a recursive form of the parameter and order estimation. The methodology developed here may be applied to an AR model of any dimension. Computer simulation results are provided to illustrate the behavior of this method

In recent years, a relationship has been suggested between the occurrence of cerebral embolism and stroke. Ultrasound has therefore become essential in the detection of emboli when monitoring cerebral vascular disorders and forms part of ultrasound brain-imaging techniques. Such detection is based on investigating the middle cerebral artery using a TransCranial Doppler (TCD) system, and analyzing the Doppler signal of the embolism. Most of the emboli detected in practical experiments are large emboli because their signatures are easy to recognize in the TCD signal. However, detection of small emboli remains a challenge. Various approaches have been proposed to solve the problem, ranging from the exclusive use of expert human knowledge to automated collection of signal parameters. Many studies have recently been performed using time-frequency distributions and classical parameter modeling for automatic detection of emboli. It has been shown that autoregressive (AR) modeling associated with an abrupt change detection technique is one of the best methods for detection of microemboli. One alternative to this is a technique based on taking expert knowledge into account. This paper aims to unite these two approaches using AR modeling and expert knowledge through a neurofuzzy approach. The originality of this approach lies in combining these two techniques and then proposing a parameter referred to as score ranging from 0 to 1. Unlike classical techniques, this score is not only a measure of confidence of detection but also a tool enabling the final detection of the presence or absence of microemboli to be performed by the practitioner. Finally, this paper provides performance evaluation and comparison with an automated technique, i.e., AR modeling used in vitro.

Use of ultrasound, namely in the biomedical diagnosis and industrial fields, pioneered in 1950s, is today particularly widespread. In the last decades, ultrasound imaging has benefited from advances in numerical technologies such as signal processing. On the other hand, the use of ultrasound imaging has increased the need for signal processing techniques. This paper presents a review and the up-to-date developments in ultrasound imaging techniques, including elementary principles, signal acquisition and processing, from one dimensional to multidimensional systems. This paper also deals with typical relevant applications.

The main purpose of this letter is to show that measurement of length is an interesting tool to characterize band-limited signals. We show the link between the length of a signal and that of the complex instantaneous frequency (CIF), and we propose original-length and instantaneous frequency estimators which we illustrate by examples.

This paper presents a improvement of high-order cumulant-based parameter estimation using delta operator applied to the instrumental variable algorithm. It is based on a modification of the classical least squares estimation and the utilization of the delta operator and the introduction of an additional term in the parameter estimates. Computer simulation results are given to illustrate the behavior of this method.

This letter presents a new recursive high order cumulant-based instrumental variable algorithm. It is based on a modification of the classical least squares estimation and the utilization of the delta operator. The algorithm provides an expression of autoregressive (AR) parameters estimation, in which an additional term appears. This results in an improvement of the convergence of the classical q operator algorithm. Computer simulation results are given to illustrate the behavior of this method.