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Statistical image reconstruction (SIR) methods have shown potential to substantially improve the image quality of low-dose X-ray computed tomography (CT) as compared to the conventional filtered back-projection (FBP) method for various…
Bar charts are among the most frequently used visualizations, in part because their position encoding leads them to convey data values precisely. Yet reproductions of single bars or groups of bars within a graph can be biased. Curiously,…
Computational ghost imaging generally requires a large number of pattern illumination to obtain a high-quality image. The colored noise speckle pattern was recently proposed to substitute the white noise pattern in a variety of noisy…
We focus on a multidimensional field with uncorrelated spectrum, and study the quality of the reconstructed signal when the field samples are irregularly spaced and affected by independent and identically distributed noise. More…
Creating geometric abstracted models from image-based scene reconstructions is difficult due to noise and irregularities in the reconstructed model. In this paper, we present a geometric modeling method for noisy reconstructions dominated…
The alignment of shapes has been a crucial step in statistical shape analysis, for example, in calculating mean shape, detecting locational differences between two shape populations, and classification. Procrustes alignment is the most…
The characterization and reconstruction of heterogeneous materials, such as porous media and electrode materials, involve the application of image processing methods to data acquired by microscopy techniques. In this study, we present a…
Mathematical methods of step-by-step and combined shifts are proposed for experimental data processing to reconstruct the measuring system impulse response distorted by shift-invariant blur. Proposed methods base on direct non-blind…
Estimation is the computational task of recovering a hidden parameter $x$ associated with a distribution $D_x$, given a measurement $y$ sampled from the distribution. High dimensional estimation problems arise naturally in statistics,…
Sparsity promoting regularization is an important technique for signal reconstruction and several other ill-posed problems. Theoretical investigation typically bases on the assumption that the unknown solution has a sparse representation…
Modern 3D semantic scene graph estimation methods utilize ground truth 3D annotations to accurately predict target objects, predicates, and relationships. In the absence of given 3D ground truth representations, we explore leveraging only…
The importance of regularization has been well established in image reconstruction -- which is the computational inversion of imaging forward model -- with applications including deconvolution for microscopy, tomographic reconstruction,…
This paper deals with the problem of estimating a slope parameter in a simple linear regression model, where independent variables have functional measurement errors. Measurement errors in independent variables, as is well known, cause…
This work is concerned with the recovery of piecewise constant images from noisy linear measurements. We study the noise robustness of a variational reconstruction method, which is based on total (gradient) variation regularization. We show…
The iterative refinement method (IRM) has been very successfully applied in many different fields for examples the modern quantum chemical calculation and CT image reconstruction. It is proved that the refinement method can create an exact…
Most blind deconvolution methods usually pre-define a large kernel size to guarantee the support domain. Blur kernel estimation error is likely to be introduced, yielding severe artifacts in deblurring results. In this paper, we first…
In brain imaging, the image acquisition and processing processes themselves are likely to introduce noise to the images. It is therefore imperative to reduce the noise while preserving the geometric details of the anatomical structures for…
One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…
We propose a simple method for estimating noise level from a single color image. In most image-denoising algorithms, an accurate noise-level estimate results in good denoising performance; however, it is difficult to estimate noise level…
Cardiovascular magnetic resonance (CMR) imaging is the gold standard for diagnosing several heart diseases due to its non-invasive nature and proper contrast. MR imaging is time-consuming because of signal acquisition and image formation…