Deep learning (DL) based methods have become increasingly attractive in image motion estimation applications. In this study we investigate the use of a noise-to-noise (N2N) training strategy for improving the robustness of a DL motion-estimation network in the presence of high imaging noise in the image data. This strategy is based on the rationale that the image motion estimated from one noisy measurement of a given image pair should be equally applicable for registering the image pair when it is obtained from a different noisy measurement. In the experiments we demonstrated the proposed approach for motion-compensated noise suppression in cardiac-gated SPECT imaging, where we utilized the image data acquired from 237 clinical cases at 50% reduced dose. The proposed N2N approach yielded an average reduction of 18.5% in the mean-squared-error (MSE) of the gate frames compared to a traditional training approach. It also achieved a more uniform performance among the different cardiac phases in spite of their statistical image variability.

Motion compensation is an effective approach for reducing motion blur and suppressing noise in cardiac gated imaging. In this work, we propose to introduce a temporal regularization measure in optimization of a deep learning (DL) network for motion compensation in cardiac-gated SPECT images. This introduced measure is used to exploit the temporal consistency in the physical motion of the myocardium among consecutive phases of the cardiac cycle. In the experiment we demonstrated this approach on a set of 197 clinical acquisitions with imaging dose reduced by $50 \%$. The results demonstrate that the proposed approach can lead to improved motion compensation accuracy among all individual gates by the DL network, with an average reduction by $6 \%$ in the mean-squared-error of the motioncompensated myocardium, indicating that the proposed approach can be more robust in combating the excessive noise level in reduced dose imaging.

In medical imaging, the gold standard for image-quality assessment is a task-based approach in which one evaluates human observer performance for a given diagnostic task (e.g., detection of a myocardial perfusion or motion defect). To facilitate practical task-based image-quality assessment, model observers are needed as approximate surrogates for human observers. In cardiac-gated SPECT imaging, diagnosis relies on evaluation of the myocardial motion as well as perfusion. Model observers for the perfusion-defect detection task have been studied previously, but little effort has been devoted toward development of a model observer for cardiac-motion defect detection. In this work, we describe two model observers for predicting human observer performance in detection of cardiac-motion defects. Both proposed methods rely on motion features extracted using previously reported deformable mesh model for myocardium motion estimation. The first method is based on a Hotelling linear discriminant that is similar in concept to that used commonly for perfusion-defect detection. In the second method, based on relevance vector machines (RVM) for regression, we compute average human observer performance by first directly predicting individual human observer scores, and then using multi reader receiver operating characteristic analysis. Our results suggest that the proposed RVM model observer can predict human observer performance accurately, while the new Hotelling motion-defect detector is somewhat less effective.

It is now widely accepted that image quality should be evaluated using task-based criteria, such as human-observer performance in a lesion-detection task. The channelized Hotelling observer (CHO) has been widely used as a surrogate for human observers in evaluating lesion detectability. In this paper, we propose that the problem of developing a numerical observer can be viewed as a system-identification or supervised-learning problem, in which the goal is to identify the unknown system of the human observer. Following this approach, we explore the possibility of replacing the Hotelling detector within the CHO with an algorithm that learns the relationship between measured channel features and human observer scores. Specifically, we develop a channelized support vector machine (CSVM) which we compare to the CHO in terms of its ability to predict human-observer performance. In the examples studied, we find that the CSVM is better able to generalize to unseen images than the CHO, and therefore may represent a useful improvement on the CHO methodology, while retaining its essential features.

We derive an estimator for the standard deviation of a Gaussian random variable that uses the maximum of two observations on the random variables. The process is repeated until the variance of the estimator or the degree of confidence reaches a predetermined level. The estimator is unbiased and consistent, and its variance is only marginally larger than the standard square root of the sum of the squares estimator. Moreover the computation of an estimate requires only a sequence of comparisons of two numbers followed by an addition.

In this paper, we explore the use of a content-adaptive mesh model (CAMM) for tomographic image reconstruction. In the proposed framework, the image to be reconstructed is first represented by a mesh model, an efficient image description based on nonuniform sampling. In the CAMM, image samples (represented as mesh nodes) are placed most densely in image regions having fine detail. Tomographic image reconstruction in the mesh domain is performed by maximum-likelihood (ML) or maximum a posteriori (MAP) estimation of the nodal values from the measured data. A CAMM greatly reduces the number of unknown parameters to be determined, leading to improved image quality and reduced computation time. We demonstrated the method in our experiments using simulated gated single photon emission computed tomography (SPECT) cardiac-perfusion images. A channelized Hotelling observer (CHO) was used to evaluate the detectability of perfusion defects in the reconstructed images, a task-based measure of image quality. A minimum description length (MDL) criterion was also used to evaluate the effect of the representation size. In our application, both MDL and CHO suggested that the optimal number of mesh nodes is roughly five to seven times smaller than the number of projection bins. When compared to several commonly used methods for image reconstruction, the proposed approach achieved the best performance, in terms of defect detection and computation time. The research described in this paper establishes a foundation for future development of a (four-dimensional) space-time reconstruction framework for image sequences in which a built-in deformable mesh model is used to track the image motion.

In this work we explore the use of a content-adaptive mesh model (CAMM) in the classical problem of image restoration. In the proposed framework, we first model the image to be restored by an efficient mesh representation. A CAMM can be viewed as a form of image representation using nonuniform samples, of which the mesh nodes (i.e., image samples) are adaptively placed according to the local content of the image. The image is then restored through estimating the model parameters (i.e., mesh nodal values) from the data. A CAMM provides a natural spatially-adaptive regularization mechanism for image restoration in that the interpolation basis functions in a CAMM have their spatial support varying with the local image content. We present some exploratory results to demonstrate the proposed approach.

In this work we present a fast procedure for content-adaptive mesh representation of vector-valued (e.g., color) images. The goal is to obtain a single mesh structure that accurately represents all the individual components of the image. The proposed method is justified by an error bound that is rigorously derived for such a representation. It employs an error-diffusion type algorithm to place the mesh nodes nonuniformly in the image domain according to the image content. Experimental results demonstrate that: (1) a compact and accurate representation for color images can be achieved at low computational cost by the proposed algorithm; and (2) joint treatment of the different image components by the proposed algorithm can result in a more accurate mesh representation than a mesh based on a single image component (such as intensity) alone.

Mesh modeling is an important problem with many applications in image processing. A key issue in mesh modeling is how to generate a mesh structure that well represents an image by adapting to its content. We propose a new approach to mesh generation, which is based on a theoretical result derived on the error bound of a mesh representation. In the proposed method, the classical Floyd-Steinberg error-diffusion algorithm is employed to place mesh nodes in the image domain so that their spatial density varies according to the local image content. Delaunay triangulation is next applied to connect the mesh nodes. The result of this approach is that fine mesh elements are placed automatically in regions of the image containing high-frequency features while coarse mesh elements are used to represent smooth areas. The proposed algorithm is noniterative, fast, and easy to implement. Numerical results demonstrate that, at very low computational cost, the proposed approach can produce mesh representations that are more accurate than those produced by several existing methods. Moreover, it is demonstrated that the proposed algorithm performs well with images of various kinds, even in the presence of noise.

In this paper we present a new approach for clustering data. The clustering metric used is the normalized cross-correlation, also known as similarity, instead of the traditionally used Euclidean distance. The main advantage of this metric is that it depends on the signal shape rather than its amplitude. Under an assumption of an exponential probability model that has several desirable properties, the expectation-maximization (EM) framework is used to derive two iterative clustering algorithms. Numerical experiments are presented using simulated data in a dynamic positron emission topography study of the brain. Initial results demonstrate that the proposed method achieves better performance than several existing clustering methods.

We propose the use of a content-adaptive volumetric mesh model for fully three-dimensional (3D) tomographic image reconstruction. In the proposed framework, the image to be reconstructed is first modeled by an efficient mesh representation. The image is then obtained through estimation of the nodal values from the measured data. The use of a mesh representation can alleviate the ill-posed nature of the reconstruction problem, thereby leading to improved quality in the reconstructed images. In addition, it reduces the data storage requirement, resulting in efficient algorithms. The proposed methods are tested using gated cardiac-perfusion images. Initial results demonstrate that the proposed approach achieves good performance when compared to several commonly used methods for image reconstruction, and produces results very rapidly.

In this work we present a fast, content-adaptive approach for three-dimensional (3D) mesh representation of volumetric images. A rigorous error bound is derived for a 3D mesh representation of a volumetric image based on the theory of function interpolation. From this result, a computationally efficient algorithm is proposed for adaptive placement of mesh nodes (hence mesh elements) in the 3D image domain according to the image content. Experimental results demonstrate that a highly compact and accurate representation of volumetric images can be achieved at low computational cost by the proposed algorithm.

While geometric attacks are one of the most challenging problems in watermarking, random bending is probably the most difficult to handle among all geometric attacks. We present a watermarking scheme based on a new deformable mesh model to combat such attacks. The distortion is corrected using the distortion field (DF) estimated by minimizing the matching error between the meshes of the original and the attacked image. A CDMA watermarking method is used for testing the proposed method, which embeds a multi-bit signature in the DCT domain and uses mesh model correction to achieve robustness. Experiments show that the proposed scheme can survive a wide range of random bending attacks.

We propose the use of a content-adaptive mesh model (CAMM) for tomographic image reconstruction. In the proposed framework, the image to be reconstructed is first modeled by an efficient mesh representation. The image is then obtained through estimation of the nodal values from the measured data. The use of a CAMM can greatly alleviate the ill-posed nature of the reconstruction problem, thereby leading to improved quality in the reconstructed images. In addition, it can lead to development of efficient numerical reconstruction algorithms. Finally, it can be useful for motion-tracking of image sequences. The proposed methods are tested using simulated gated cardiac-perfusion SPECT images. Our results indicate that, among the methods tested, the proposed approach achieves the best performance in terms of image quality and computation time, and can also reduce the memory requirement.

Previously, we proposed a computationally efficient approach to content-adaptive mesh generation used for image representation (see Lee, J. et al., IEEE Int. Conf. Image Proc., 2000). We now provide a theoretical basis for that method, which leads to an improved version of the algorithm. An error bound is derived for a mesh representation of an image based on the theory of function interpolation. From this result, a more accurate scheme is proposed for placement of mesh elements in the image domain according to the image content. Experimental results, compared to other methods, show that a highly accurate image representation can be obtained at extremely low computational cost by the proposed technique.

In tomographic image reconstruction, it is usually assumed that the system matrix is known exactly, although this is not usually the case in practice. We investigate the potential benefit of modeling the system matrix as the sum of a known part and an unknown random error. Using some of simplifying assumptions, we develop a penalized weighted least squares (PWLS) reconstruction algorithm for this problem. Our experiments indicate that this approach can, indeed lead to significant improvements in the reconstructed image, both visually and quantitatively.