In linear approximation, the formation of a radio-frequency (RF) ultrasound image can be described based on a standard convolution model in which the image is obtained as a result of convolution of the point spread function (PSF) of the ultrasound scanner in use with a tissue reflectivity function (TRF). Due to the band-limited nature of the PSF, the RF images can only be acquired at a finite spatial resolution, which is often insufficient for proper representation of the diagnostic information contained in the TRF. One particular way to alleviate this problem is by means of image deconvolution, which is usually performed in a “blind” mode, when both PSF and TRF are estimated at the same time. Despite its proven effectiveness, blind deconvolution (BD) still suffers from a number of drawbacks, chief among which stems from its dependence on a stationary convolution model, which is incapable of accounting for the spatial variability of the PSF. As a result, virtually all existing BD algorithms are applied to localized segments of RF images. In this work, we introduce a novel method for non-stationary BD, which is capable of recovering the TRF concurrently with the spatially variable PSF. Particularly, our approach is based on semigroup theory which allows one to describe the effect of such a PSF in terms of the action of a properly defined linear semigroup. The approach leads to a tractable optimization problem, which can be solved using standard numerical methods. The effectiveness of the proposed solution is supported by experiments with in vivo ultrasound data.
The world’s aging population has given rise to an increasing awareness towards neurodegenerative disorders, including Alzheimers Disease (AD). Treatment options for AD are currently limited, but it is believed that future success depends on our ability to detect the onset of the disease in its early stages. The most frequently used tools for this include neuropsychological assessments, along with genetic, proteomic, and image-based diagnosis. Recently, the applicability of Diffusion Magnetic Resonance Imaging (dMRI) analysis for early diagnosis of AD has also been reported. The sensitivity of dMRI to the microstructural organization of cerebral tissue makes it particularly well-suited to detecting changes which are known to occur in the early stages of AD. Existing dMRI approaches can be divided into two broad categories: region-based and tract-based. In this work, we propose a new approach, which extends region-based approaches to the simultaneous characterization of multiple brain regions. Given a predefined set of features derived from dMRI data, we compute the probabilistic distances between different brain regions and treat the resulting connectivity pattern as an undirected, fully-connected graph. The characteristics of this graph are then used as markers to discriminate between AD subjects and normal controls (NC). Although in this preliminary work we omit subjects in the prodromal stage of AD, mild cognitive impairment (MCI), our method demonstrates perfect separability between AD and NC subject groups with substantial margin, and thus holds promise for fine-grained stratification of NC, MCI and AD populations.
Multi-shell diffusion imaging (MSDI) allows to characterize the subtle tissue properties of neurons along with providing valuable information about the ensemble average diffusion propagator. Several methods, both para- metric and non-parametric, have been proposed to analyze MSDI data. In this work, we propose a hybrid model, which is non-parametric in the angular domain but parametric in the radial domain. This has the advantage of allowing arbitrary number of fiber orientations in the angular domain, yet requiring as little as two b-value shells in the radial (q-space) domain. Thus, an extensive sampling of the q-space is not required to compute the diffusion propagator. This model, which we term as the dual-spherical" model, requires estimation of two functions on the sphere to completely (and continuously) model the entire q-space diffusion signal. Specifically, we formulate the cost function so that the diffusion signal is guaranteed to monotonically decrease with b-value for user-defined range of b-values. This is in contrast to other methods, which do not enforce such a constraint, resulting in in-accurate modeling of the diffusion signal (where the signal values could potentially increase with b-value). We also show the relation of our proposed method with that of diffusional kurtosis imaging and how our model extends the kurtosis model. We use the standard spherical harmonics to estimate these functions on the sphere and show its efficacy using synthetic and in-vivo experiments. In particular, on synthetic data, we computed the normalized mean squared error and the average angular error in the estimated orientation distribution function (ODF) and show that the proposed technique works better than the existing work which only uses a parametric model for estimating the radial decay of the diffusion signal with b-value.
KEYWORDS: Spherical lenses, Signal to noise ratio, Deconvolution, Data modeling, Error analysis, Brain, Diffusion, High angular resolution imaging, Diffusion tensor imaging, Magnetic resonance imaging
High angular resolution diffusion imaging (HARDI) improves upon more traditional diffusion tensor imaging (DTI) in its ability to resolve the orientations of crossing and branching neural fibre tracts. The HARDI signals are measured over a spherical shell in q-space, and are usually used as an input to q-ball imaging (QBI) which allows estimation of the diffusion orientation distribution functions (ODFs) associated with a given region-of interest. Unfortunately, the partial nature of single-shell sampling imposes limits on the estimation accuracy. As a result, the recovered ODFs may not possess sufficient resolution to reveal the orientations of fibre tracts which cross each other at acute angles. A possible solution to the problem of limited resolution of QBI is provided by means of spherical deconvolution, a particular instance of which is sparse deconvolution. However, while capable of yielding high-resolution reconstructions over spacial locations corresponding to white matter, such methods tend to become unstable when applied to anatomical regions with a substantial content of isotropic diffusion. To resolve this problem, a new deconvolution approach is proposed in this paper. Apart from being uniformly stable across the whole brain, the proposed method allows one to quantify the isotropic component of cerebral diffusion, which is known to be a useful diagnostic measure by itself.
Non-local means (NLM) filtering has been shown to outperform alternative denoising methodologies under the model of additive white Gaussian noise contamination. Recently, several theoretical frameworks have been developed to extend this class of algorithms to more general types of noise statistics. However, many of these frameworks are specifically designed for a single noise contamination model, and are far from optimal across varying noise statistics. The NLM filtering techniques rely on the definition of a similarity measure, which quantifies the similarity of two neighbourhoods along with their respective centroids. The key to the unification of the NLM filter for different noise statistics lies in the definition of a universal similarity measure which is guaranteed to provide favourable performance irrespective of the statistics of the noise. Accordingly, the main contribution of this work is to provide a rigorous statistical framework to derive such a universal similarity measure, while highlighting some of its theoretical and practical favourable characteristics. Additionally, the closed form expressions of the proposed similarity measure are provided for a number of important noise scenarios and the practical utility of the proposed similarity measure is demonstrated through numerical experiments.
The advent of the theory of compressed sensing (CS) has revolutionized multiple areas of applied sciences, a
particularly important instance of which is medical imaging. In particular, the theory provides a solution to the
problem of long acquisition times, which is intrinsic in diffusion MRI (dMRI). As a specific instance of dMRI,
this work focuses on high angular resolution diffusion imaging (HARDI), which is known to excel in delineating
multiple diffusion flows through a given voxel within the brain. Specifically, to reduce the acquisition time, CS
allows undersampling the HARDI data by employing fewer diffusion-encoding gradients than it is required by the
classical sampling theory. Subsequently, the undersampled data is used to recover the original signals by means
of non-linear decoding. In earlier reconstruction methods, such decoding has been carried out under a Gaussian
model for measurement noises, instead of the Rician model which is known to prevail in MRI. Accordingly,
the main contribution of the present work is twofold. First, we introduce a way to substantially improve the
stability of the CS-based reconstruction of HARDI signals under the assumption of Gaussian noises. Second, we
extend this approach to the case of Rician noise statistics. In addition to providing formal developments of the
reconstruction algorithm based on Rician statistics, we also detail a computationally efficient numerical scheme
which can be used to implement the above reconstruction. Finally, the methods based on the Gaussian and
the Rician noise models are compared using both simulated and in-vivo MRI data under various measurement
conditions.
KEYWORDS: Denoising, Spherical lenses, Signal to noise ratio, Linear filtering, Diffusion, Digital filtering, Electronic filtering, Brain, Diffusion magnetic resonance imaging, In vivo imaging
Diffusion MRI (dMRI) is a unique imaging modality for in vivo delineation of the anatomical structure of white
matter in the brain. In particular, high angular resolution diffusion imaging (HARDI) is a specific instance of
dMRI which is known to excel in detection of multiple neural fibers within a single voxel. Unfortunately, the
angular resolution of HARDI is known to be inversely proportional to SNR, which makes the problem of denoising
of HARDI data be of particular practical importance. Since HARDI signals are effectively band-limited, denoising
can be accomplished by means of linear filtering. However, the spatial dependency of diffusivity in brain tissue
makes it impossible to find a single set of linear filter parameters which is optimal for all types of diffusion
signals. Hence, adaptive filtering is required. In this paper, we propose a new type of non-local means (NLM)
filtering which possesses the required adaptivity property. As opposed to similar methods in the field, however,
the proposed NLM filtering is applied in the spherical domain of spatial orientations. Moreover, the filter uses
an original definition of adaptive weights, which are designed to be invariant to both spatial rotations as well
as to a particular sampling scheme in use. As well, we provide a detailed description of the proposed filtering
procedure, its efficient implementation, as well as experimental results with synthetic data. We demonstrate
that our filter has substantially better adaptivity as compared to a number of alternative methods.
Prostate specific antigen density is an established parameter for indicating the likelihood of prostate cancer. To
this end, the size and volume of the gland have become pivotal quantities used by clinicians during the standard
cancer screening process. As an alternative to manual palpation, an increasing number of volume estimation
methods are based on the imagery data of the prostate. The necessity to process large volumes of such data
requires automatic segmentation algorithms, which can accurately and reliably identify the true prostate region.
In particular, transrectal ultrasound (TRUS) imaging has become a standard means of assessing the prostate
due to its safe nature and high benefit-to-cost ratio. Unfortunately, modern TRUS images are still plagued by
many ultrasound imaging artifacts such as speckle noise and shadowing, which results in relatively low contrast
and reduced SNR of the acquired images. Consequently, many modern segmentation methods incorporate prior
knowledge about the prostate geometry to enhance traditional segmentation techniques. In this paper, a novel
approach to the problem of TRUS segmentation, particularly the definition of the prostate shape prior, is
presented. The proposed approach is based on the concept of distribution tracking, which provides a unified
framework for tracking both photometric and morphological features of the prostate. In particular, the tracking
of morphological features defines a novel type of "weak" shape priors. The latter acts as a regularization force,
which minimally bias the segmentation procedure, while rendering the final estimate stable and robust. The value of the proposed methodology is demonstrated in a series of experiments.
Image segmentation and tissue characterization are fundamental tasks of computer-aided diagnosis (CAD) in
medical ultrasound imaging. As an initial step, such algorithms are usually based on extraction of pertinent
features from the acquired ultrasound data. Typically, these features are computed directly from localized
image segments, thereby representing local statistical properties of the image. However, the process of image
formation of medical ultrasound suggests that such an approach could result in a variety of unwanted artifacts
(such as excessively smooth segmentation boundaries or misclassification) at subsequent stages of the algorithm.
In this work, we propose to first decompose the observed images into a number of their statistically distinct
components. The decomposition is based on the maximum-a-posteriori (MAP) statistical framework which has
been derived based on the signal and noise models appropriate for the ultrasound setting. Subsequently, each
resulting component is used separately to extract a set of its corresponding features. When retrieved in this way
(rather than directly from the observed image), the combined set of resulting features is shown to be capable of
better discriminating between different tissue types. Examples of in silico simulations and in vivo experiments
are provided to illustrate the practical usefulness of this technique for improving the results of ultrasound image
segmentation.
The tracking algorithm is presented that reduces the influence of the camera motion on the tracking performance. The algorithm uses a change detector. The target motion is described by parameterized optical flow. The flow parameters are estimated using Kalman filtering. The algorithm allows us to estimate the target motion without any bias associated with the camera motion. The effects of thermal blooming on high-energy laser beacon for air-to-ground directed energy system are evaluated. The laser fluence at the target and power in the bucket are evaluated for various tactical engagement scenarios and different atmospheric conditions. The critical laser power that can be efficiently transmitted through the atmosphere is evaluated. Two techniques for mitigating the effects of thermal blooming including a method based on pointing of a high energy beam "downwind" to correct for the thermal blooming tilt and focusing a high energy beam beyond the target range are evaluated. We found that the power in the bucket at the target at the optical axis of a high energy beam for tactical directed energy system increases about one order of magnitude due to correction of the thermal blooming tilt.
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