A plethora of techniques for cardiac deformation imaging with 3D ultrasound, typically referred to as 3D speckle tracking techniques, are available from academia and industry. Although the benefits of single methods over alternative ones have been reported in separate publications, the intrinsic differences in the data and definitions used makes it hard to compare the relative performance of different solutions. To address this issue, we have recently proposed a framework to simulate realistic 3D echocardiographic recordings and used it to generate a common set of ground-truth data for 3D speckle tracking algorithms, which was made available online. The aim of this study was therefore to use the newly developed database to contrast non-commercial speckle tracking solutions from research groups with leading expertise in the field. The five techniques involved cover the most representative families of existing approaches, namely block-matching, radio-frequency tracking, optical flow and elastic image registration. The techniques were contrasted in terms of tracking and strain accuracy. The feasibility of the obtained strain measurements to diagnose pathology was also tested for ischemia and dyssynchrony.

Recurrence of small clean image patches across different scales of a natural image has been successfully used for solving ill-posed problems in clean images (e.g., super-resolution from a single image). In this paper we show how this multi-scale property can be extended to solve ill-posed problems under noisy conditions, such as image denoising. While clean patches are obscured by severe noise in the original scale of a noisy image, noise levels drop dramatically at coarser image scales. This allows for the unknown hidden clean patches to "naturally emerge" in some coarser scale of the noisy image. We further show that patch recurrence across scales is strengthened when using directional pyramids (that blur and sub sample only in one direction). Our statistical experiments show that for almost any noisy image patch (more than 99%), there exists a "good" clean version of itself at the same relative image coordinates in some coarser scale of the image. This is a strong phenomenon of noise-contaminated natural images, which can serve as a strong prior for separating the signal from the noise. Finally, incorporating this multi-scale prior into a simple denoising algorithm yields state-of-the-art denoising results.

Image denoising methods can broadly be classified into two types: “Internal Denoising” (denoising an image patch using other noisy patches within the noisy image), and “External Denoising” (denoising a patch using external clean natural image patches). Any such method, whether Internal or External, is typically applied to all image patches. In this paper we show that different image patches inherently have different preferences for Internal or External de-noising. Moreover, and surprisingly, the higher the noise in the image, the stronger the preference for Internal De-noising. We identify and explain the source of this behavior, and show that Internal/External preference of a patch is directly related to its individual Signal-to-Noise-Ratio (“PatchSNR”). Patches with high PatchSNR (e.g., patches on strong edges) benefit much from External Denoising, whereas patches with low PatchSNR (e.g., patches in noisy uniform regions) benefit much more from Internal Denoising. Combining the power of Internal or External denoising selectively for each patch based on its estimated PatchSNR leads to improvement in denoising performance.

Statistics of `natural images' provides useful priors for solving under-constrained problems in Computer Vision. Such statistics is usually obtained from large collections of natural images. We claim that the substantial internal data redundancy within a single natural image (e.g., recurrence of small image patches), gives rise to powerful internal statistics, obtained directly from the image itself. While internal patch recurrence has been used in various applications, we provide a parametric quantification of this property. We show that the likelihood of an image patch to recur at another image location can be expressed parametricly as a function of the spatial distance from the patch, and its gradient content. This “internal parametric prior” is used to improve existing algorithms that rely on patch recurrence. Moreover, we show that internal image-specific statistics is often more powerful than general external statistics, giving rise to more powerful image-specific priors. In particular: (i) Patches tend to recur much more frequently (densely) inside the same image, than in any random external collection of natural images. (ii) To find an equally good external representative patch for all the patches of an image, requires an external database of hundreds of natural images. (iii) Internal statistics often has stronger predictive power than external statistics, indicating that it may potentially give rise to more powerful image-specific priors.