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

Estimating blood vessel areas in ultrasound images using a deformable template model

We consider the problem of obtaining interval estimates of vessel areas from ultrasound images of cross sections through the carotid artery. Robust and automatic estimates of the cross sectional area is of medical interest and of help in diagnosing atherosclerosis, which is caused by plaque deposits in the carotid artery. We approach this problem by using a deformable template to model the blood vessel outline, and use recent developments in ultrasound science to model the likelihood. We demonstrate that by using an explicit model for the outline, we can easily adjust for an important feature in the data: strong edge reflections called specular reflection. The posterior is challenging to explore, and naive standard MCMC algorithms simply converge too slowly. To obtain an efficient MCMC algorithm we make extensive use of computational efficient Gaussian Markov random fields, and use various block sampling constructions that jointly update large parts of the model.

Coherent-array imaging using phased subarrays. Part I: basic principles

The front-end hardware complexity of a coherent array imaging system scales with the number of active array elements that are simultaneously used for transmission or reception of signals. Different imaging methods use different numbers of active channels and data collection strategies. Conventional full phased array (FPA) imaging produces the best image quality using all elements for both transmission and reception, and it has high front-end hardware complexity. In contrast, classical synthetic aperture (CSA) imaging only transmits on and receives from a single element at a time, minimizing the hardware complexity but achieving poor image quality. We propose a new coherent array imaging method--phased subarray (PSA) imaging--that performs partial transmit and receive beam-forming using a subset of adjacent elements at each firing step. This method reduces the number of active channels to the number of subarray elements; these channels are multiplexed across the full array and a reduced number of beams are acquired from each subarray. The low-resolution subarray images are laterally upsampled, interpolated, weighted, and coherently summed to form the final high-resolution PSA image. The PSA imaging reduces the complexity of the front-end hardware while achieving image quality approaching that of FPA imaging.

Shift-invariant, DWT-based "projection" method for estimation of ultrasound pulse power spectrum

An approach to computing estimates of the ultrasound pulse spectrum from echo-ultrasound RF sequences, measured from biological tissues, is proposed. It is computed by a "projection" algorithm based on the Discrete Wavelet Transform (DWT) using averaging over a range of linear shifts. It is shown that the robust, shift invariant estimate of the ultrasound pulse power spectrum can be obtained by the projection of RF line log spectrum on an appropriately chosen subspace of L2(R) (i.e., the space of square-integrable functions) that is spanned by a redundant collection of compactly supported, scaling functions. This redundant set is formed from the traditional (in Wavelet analysis) orthogonal set of scaling functions and also by all its linear (discrete) shifts. A proof is given that the estimate, so obtained, could be viewed as the average of the orthogonal projections of the RF line log spectrum, computed for all significant linear shifts of the RF line log spectrum in frequency domain. It implies that the estimate is shift-invariant. A computationally efficient scheme is presented for calculating the estimate. Proof is given that the averaged, shift-invariant estimate can be obtained simply by a convolution with a kernel, which can be viewed as the discretized auto-correlation function of the scaling function, appropriate to the particular subspace being considered. It implies that the computational burden is at most O(n log2 n), where n is the problem size, making the estimate quite suitable for real-time processing. Because of the property of the wavelet transform to suppress polynomials of orders lower than the number of the vanishing moments of the wavelet used, the presented approach can be considered as a local polynomial fitting. This locality plays a crucial role in the performance of the algorithm, improving the robustness of the estimation. Moreover, it is shown that the "averaging" nature of the proposed estimation allows using (relatively) poorly regular wavelets (i.e., short filters), without affecting the estimation quality. The latter is of importance whenever the number of calculations is crucial.

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.