Two-dimensional noise-robust blind deconvolution of ultrasound images

This paper presents a new method for 2-D blind homomorphic deconvolution of medical B-scan ultrasound images. The method is based on noise-robust 2-D phase unwrapping and a noise-robust procedure to estimate the pulse in the complex cepstrum domain. Ordinary Wiener filtering is used in the subsequent deconvolution. The resulting images became much sharper with better defined tissue structures compared with the ordinary images. The deconvolved images had a resolution gain of the order of 3 to 7, and the signal-to-noise ratio (SNR) doubled for many of the images used in our experiments. The method gave stable results with respect to noise and gray levels through several image sequences     

Noise robust one-dimensional blind deconvolution of medical ultrasound images

Recently, several blind cepstral deconvolution methods for medical ultrasound images were compared experimentally. The results indicated that the generalized cepstrum or the complex cepstrum with phase unwrapping give the blind homomorphic deconvolution algorithms with the best performance. However, the frequency domain phase unwrapping for pulse estimation, which is an essential part of both methods, is sensitive to the sensor noise when the values of the spectrum are small due to the randomness of the tissue response. The noise introduces abrupt changes in the phase. The phase degradation due to the noise causes variable spatial and gray scale resolution in image sequences following deconvolution. This paper introduces a noise robust Bayesian phase unwrapping method using a noncausal Markov random chain model. The prior regularizing term accounts for the noise and smoothes the phase. The phase unwrapping is formulated as a least mean square optimization problem. The optimization is done noniteratively by solving a difference equation using the cosine transform. The resulting improvement in radial and lateral blind deconvolution is demonstrated on six short ultrasound image sequences recorded in vitro or in vivo.     

Three-dimensional blind deconvolution of ultrasound images

Three-dimensional ultrasound images are blurred by the ultrasound pulse through the convolution between the 3-D tissue signal and the 3-D pulse. The blurring reduces the spatial resolution of the 3-D ultrasound images and, consequently, their diagnostic value. This paper presents a method for 3-D blind homomorphic deconvolution of medical 3-D ultrasound images to improve their spatial resolution. The blind estimate of the 3-D pulse is necessary because the pulse changes in spatial extent and frequency composition as it passes through the tissues and because the pulse is not separable in its spatial dimensions. The method was tested on a 3-D image of a phantom with anechoic spheres of known size in a uniform diffuse scattering matrix. The spheres were clearly better defined and had volumes much closer to the true volume in the deconvolved image than in the original image     

Restoration of medical ultrasound images using two-dimensionalhomomorphic deconvolution

Describes how two-dimensional (2D) homomorphic deconvolution can be used to improve the lateral and radial resolution of medical ultrasound images recorded by a sector scanner. The recorded radio frequency ultrasound image in polar coordinates is considered as a 2D sequence of angle and depth convolved with a 2D space invariant point-spread function (PSF). Each polar coordinate sequence is transformed into the 2D complex cepstrum domain using the fast Fourier transform for Cartesian coordinates. The low-angle and low-depth portion of this sequence is taken as an estimate of the complex cepstrum representation of the PSF. It is transformed back to the Fourier frequency domain and is used to compute the deconvolved angle and depth sequence by 2D Wiener filtering. Two-dimensional homomorphic deconvolution produced substantial improvement in the resolution of B-mode images of a tissue-mimicking phantom in vitro and of several human tissues in vivo. It was better than lateral or radial homomorphic deconvolution alone, and better than 2D Wiener filtering with a PSF recorded in vitro     

Multiframe blind deconvolution of heavily blurred astronomical images

A multichannel blind deconvolution algorithm that incorporates the maximum-likelihood image restoration by several estimates of the differently blurred point-spread function (PSF) into the Ayers-Dainty iterative algorithm is proposed. The algorithm uses no restrictions on the image and the PSFs except for the assumption that they are positive. The algorithm employs no cost functions, input parameters, a priori probability distributions, or the analytically specified transfer functions. The iterative algorithm permits its application in the presence of different kinds of distortion. The work presents results of digital modeling and the results of processing real telescope data from several satellites. The proof of convergence of the algorithm to the positive estimates of object and the PSFs is given. The convergence of the Ayers-Dainty algorithm with a single processed frame is not obvious in the general case; therefore it is useful to have confidence in its convergence in a multiframe case. The dependence of convergence on the number of processed frames is discussed. Formulas for evaluating the quality of the algorithm performance on each iteration and the rule of stopping its work in accordance with this quality are proposed. A method of building the monotonically converging subsequence of the image estimates of all the images obtained in the iterative process is also proposed.     

Comparison of direct blind deconvolution methods for motion-blurred images

Direct methods for restoration of images blurred by motion are analyzed and compared. The term direct means that the considered methods are performed in a one-step fashion without any iterative technique. The blurring point-spread function is assumed to be unknown, and therefore the image restoration process is called blind deconvolution. What is believed to be a new direct method, here called the whitening method, was recently developed. This method and other existing direct methods such as the homomorphic and the cepstral techniques are studied and compared for a variety of motion types. Various criteria such as quality of restoration, sensitivity to noise, and computation requirements are considered. It appears that the recently developed method shows some improvements over other older methods. The research presented here clarifies the differences among the direct methods and offers an experimental basis for choosing which blind deconvolution method to use. In addition, some improvements on the methods are suggested.     

Higher order spectra based deconvolution of ultrasound images

We address the problem of improving the spatial resolution of ulrasound images through blind deconvolution. The ultrasound image formation process in the RF domain can be expressed as a spatio-temporal convolution between the tissue response and the ultrasonic system response, plus additive noise. Convolutional components of the dispersive attenuation and aberrations introduced by propagating through the object being imaged are also incorporated in the ultrasonic system response. Our goal is to identify and remove the convolutional distortion in order to reconstruct the tissue response, thus enhancing the diagnostic quality of the ultrasonic image. Under the assumption of an independent, identically distributed, zero-mean, non-Gaussian tissue response, we were able to estimate distortion kernels using bicepstrum operations on RF data. Separate 1D distortion kernels were estimated corresponding to axial and lateral image lines and used in the deconvolution process. The estimated axial kernels showed similarities to the experimentally measured pulse-echo wavelet of the imaging system. Deconvolution results from B-scan images obtained with clinical imaging equipment showed a 2.5-5.2 times gain in lateral resolution, where the definition of the resolution has been based on the width of the autocovariance function of the image. The gain in axial resolution was found to be between 1.5 and 1.9     

Initialization of iterative parametric algorithms for blind deconvolution of motion-blurred images

Performances of iterative blind deconvolution methods for motion-blurred images are usually reduced depending on the accuracy of the required initial guess of the blur. We examine this dependency, and a two-stage restoration procedure is proposed: First we perform a direct technique with a single straight-forward process to produce a rough initial estimate of the blur, and then an iterative technique is employed to refine the blur estimate. Two common iterative techniques (the expectation-maximization and the Richardson-Lucy methods) are examined here and implemented in the combined direct-iterative modification for a variety of motion blur types. Results show that the combined method significantly improves the reliability of the deconvolution process.     

傅里叶-小波正则反卷积医学超声成像方法

研究了利用傅里叶-小波正则反卷积改善医学超声图像质量的方法。将高阶谱方法和傅里叶-小波正则反卷积算法创新地用于医用超声诊断仪的轴向和纵向的二维射频信号,首先估计出中心频率为3.5MHz的A扫描系统函数,然后应用对射频A扫信号进行反卷积成像。实验结果表明,该方法显著改善了因系统函数与被测信号卷积所产生的分辨率退化现象,极大地提高了医学超声图像的分辨率和信噪比。     

Despeckling of medical ultrasound images

Speckle noise is an inherent property of medical ultrasound imaging, and it generally tends to reduce the image resolution and contrast, thereby reducing the diagnostic value of this imaging modality. As a result, speckle noise reduction is an important prerequisite, whenever ultrasound imaging is used for tissue characterization. Among the many methods that have been proposed to perform this task, there exists a class of approaches that use a multiplicative model of speckled image formation and take advantage of the logarithmical transformation in order to convert multiplicative speckle noise into additive noise. The common assumption made in a dominant number of such studies is that the samples of the additive noise are mutually uncorrelated and obey a Gaussian distribution. The present study shows conceptually and experimentally that this assumption is oversimplified and unnatural. Moreover, it may lead to inadequate performance of the speckle reduction methods. The study introduces a simple preprocessing procedure, which modifies the acquired radio-frequency images (without affecting the anatomical information they contain), so that the noise in the log-transformation domain becomes very close in its behavior to a white Gaussian noise. As a result, the preprocessing allows filtering methods based on assuming the noise to be white and Gaussian, to perform in nearly optimal conditions. The study evaluates performances of three different, nonlinear filters--wavelet denoising, total variation filtering, and anisotropic diffusion--and demonstrates that, in all these cases, the proposed preprocessing significantly improves the quality of resultant images. Our numerical tests include a series of computer-simulated and in vivo experiments.     

Bayesian 2-D deconvolution: a model for diffuse ultrasound scattering

Observed medical ultrasound images are degraded representations of the true acoustic tissue reflectance. The degradation is due to blur and speckle and significantly reduces the diagnostic value of the images. To remove both blur and speckle, we have developed a new statistical model for diffuse scattering in 2-D ultrasound radio frequency images, incorporating both spatial smoothness constraints and a physical model for diffuse scattering. The modeling approach is Bayesian in nature, and we use Markov chain Monte Carlo methods to obtain the restorations. The results from restorations of some real and simulated radio frequency ultrasound images are presented and compared with results produced by Wiener filtering     

Comparison of cepstrum-based methods for radial blind deconvolutionof ultrasound images

This paper compares the performance of seven different cepstrum-based methods for radial blind deconvolution of medical ultrasound images. The first is the generalized cepstrum method. The second is the spectral root cepstrum method. These methods have received little attention so far. The last five methods are all based on the complex cepstrum, but different computational techniques in the spatial and frequency domain are employed. Using in vivo radio frequency data from a clinical scanner, the generalized cepstrum method gave the best images closely followed by the complex cepstrum using phase unwrapping or polynomial rooting. The complex cepstrum method using higher-order statistics was ranked as low as number five. These results are an important guideline for selecting a specific cepstrum-based radial deconvolution method for implementation in ultrasound scanners     

Robust deconvolution of high-frequency ultrasound images using higher-order spectral analysis and wavelets

Deconvolution of high-frequency (30-40 MHz) ultrasonic images of human skin was studied in vivo. Separate one-dimensional (1-D) functions for the axial and lateral profiles were first estimated using higher-order spectral methods. Subsequently, deconvolution was implemented using a regularized inverse Wiener filtering of the wavelet and scaling coefficients that were obtained after a wavelet decomposition of the RF signals. Deconvolution was first performed in the axial direction, then in the lateral direction. The methods were applied to data obtained from the skin of 16 volunteers using three different transducers. Significant improvements in both the axial and lateral resolutions were obtained in all the cases. Features such as hair follicles in the dermis and fingerprints on the surface of the finger were more clearly displayed in the processed images compared to the original images. The results indicate that the deconvolution method using higher-order spectral methods and wavelet analysis could significantly improve the quality of high-frequency ultrasonic skin images.     

Multichannel blind deconvolution of polarimetric imagery

A maximum likelihood blind deconvolution algorithm is derived for incoherent polarimetric imagery using expectation maximization. In this approach, the unpolarized and fully polarized components of the scene are estimated along with the corresponding angles of polarization and channel point spread functions. The scene state of linear polarization is determined unambiguously using this parameterization. Results are demonstrated using laboratory data.     

Bayesian 2-D deconvolution: effect of using spatially invariant ultrasound point spread functions

Observed ultrasound images are degraded representations of the true tissue reflectance. The specular reflections at boundaries between regions of different tissue types are blurred, and the diffuse scattering within homogenous regions causes speckle because of the oscillating nature of the transmitted pulse. To reduce both blur and speckle, we have developed algorithms for the restoration of simulated and real ultrasound images based on Markov random field models and Bayesian statistical methods. The algorithm is summarized here. Because the point spread function (psf) is unknown, we investigate the effects of using incorrect frequencies and sizes for the model psf during the restoration process. First, we degrade the images either with a known simulated psf or a measured psf. Then, we use different psf shapes during restoration to study the robustness of the method. We found that small variations in the parameters characterizing the psf, less than ±25% change in frequency, width, or length, still yielded satisfactory results. When altering the psf more than this, the restorations were not acceptable. The restorations were particularly sensitive to large increases in the restoring psf frequency. Thus, 2-D Bayesian restoration using a fixed psf may yield acceptable results as long as the true variant psfs have not varied too much during imaging     

Sparse deconvolution of B-scan images

In this paper, a new computationally efficient sparse deconvolution algorithm for the use on B-scan images from objects with relatively few scattering targets is presented. It is based on a linear image formation model that has been used earlier in connection with linear minimum mean squared error (MMSE) two-dimensional (2-D) deconvolution. The MMSE deconvolution results have shown improved resolution compared to synthetic aperture focusing technique (SAFT), but at the cost of increased computation time. The proposed algorithm uses the sparsity of the image, reducing the degrees of freedom in the reconstruction problem, to reduce the computation time and to improve the resolution. The dominating task in the algorithm consists in detecting the set of active scattering targets, which is done by iterating between one up-dating pass that detects new points to include in the set, and a down-dating pass that removes redundant points. In the up-date, a spatiotemporal matched filter is used to isolate potential candidates. A subset of those are chosen using a detection criterion. The amplitudes of the detected scatterers are found by MMSE. The algorithm properties are illustrated using synthetic and real B-scan. The results show excellent resolution enhancement- and noise-suppression capabilities. The involved computation times are analyzed.     

High-order cumulant-based blind deconvolution of Raman spectra

The spectra recorded by a dispersion spectrophotometer are usually distorted by the response function of the instrument. To improve the resolving power, double or triple cascade spectrophotometers with narrow slits have been employed, but the total flux of the radiation available decreases accordingly, resulting in a low signal-to-noise ratio and a longer measuring time. The actual spectra can be restored approximately by mathematically removing the effects of the measuring instruments. Based on the Shalvi-Weinstein criterion, a (6, 2)-order normalized cumulant-based blind deconvolution algorithm for Raman spectral data is proposed. The actual spectral data and the unit-impulse response of the measuring instruments can be estimated simultaneously. By conducting experiments on real Raman spectra of some organic compounds, it is shown that this algorithm has a robust performance and fast convergence behavior and can improve the resolving power and correct the relative intensity distortion considerably.     

Two-dimensional arrays for medical ultrasound using multilayer flexible circuit interconnection

The development of 2-D array transducers has received much recent interest. Unfortunately, fabrication of high density 2-D arrays is difficult due to the large number of electrical interconnections which must be made to the back side of the elements. A typical array operating at 2.2 MHz may have 256 or more connections within a 16.4 mm circular footprint. Interconnection becomes even more challenging as operating frequencies increase. To solve this problem, we have developed a multilayer flexible (MLF) circuit interconnect consisting of a polyimide dielectric with inter-laminar vias routing signals vertically and etched metal traces routing signals horizontally. A transducer is fabricated from an MLF by bonding a PZT chip to its surface and dicing the chip into individual elements, with the saw kerf extending partially into the top polyimide layer to ensure physical and electrical isolation of the elements. The KLM model was used to compare the performance of an MLF 2-D array to a conventional hand wired 2-D array. MLF and wire guide transducers were fabricated, each with 256 active elements, 0.4 mm interelement spacing, and 2.2 MHz center frequency. Vector impedance, pulse length, bandwidth, angular response, and cross-coupling were found to be comparable in both types of arrays. Using the MLF, however, fabrication time was reduced dramatically. More importantly, MLF technology may be used to increase 2-D array connection density beyond the limitations of current of hand wired fabrication techniques. Thus MLF circuits provide a means for the interconnection of current and future high frequency 2-D arrays.     

Anisoplanatic deconvolution of adaptive optics images

A modified method for maximum-likelihood deconvolution of astronomical adaptive optics images is presented. By parametrizing the anisoplanatic character of the point-spread function (PSF), a simultaneous optimization of the spatially variant PSF and the deconvolved image can be performed. In the ideal case of perfect information, it is shown that the algorithm is able to perfectly cancel the adverse effects of anisoplanatism down to the level of numerical precision. Exploring two different modes of deconvolution (using object bases of pixel values or stellar field parameters), we then quantify the performance of the algorithm in the presence of Poissonian noise for crowded and noncrowded stellar fields.     

Iterative statistical approach to blind image deconvolution

Image deblurring has long been modeled as a deconvolution problem. In the literature, the point-spread function (PSF) is often assumed to be known exactly. However, in practical situations such as image acquisition in cameras, we may have incomplete knowledge of the PSF. This deblurring problem is referred to as blind deconvolution. We employ a statistical point of view of the data and use a modified maximum a posteriori approach to identify the most probable object and blur given the observed image. To facilitate computation we use an iterative method, which is an extension of the traditional expectation-maximization method, instead of direct optimization. We derive separate formulas for the updates of the estimates in each iteration to enhance the deconvolution results, which are based on the specific nature of our a priori knowledge available about the object and the blur.