Optimal restoration of noisy 3D X-ray data via shearlet

decomposition

Improved Radon Based Imaging using the Shearlet Transform

Many imaging modalities, such as Synthetic Aperture Radar (SAR), can be described mathematically as collecting data in a Radon transform domain. The process of inverting the Radon transform to form an image can be unstable when the data collected contain noise so that the inversion needs to be regularized in some way. In this work, we develop a method for inverting the Radon transform using a shearlet-based decomposition, which provides a regularization that is nearly optimal for a general class of images. We then show through a variety of examples that this technique performs better than similar competitive methods based on the use of the wavelet and the curvelet transforms. 1

Multi-Composite Wavelet Estimation

In this work, we present a new approach to image denoising derived from the general framework of wavelets with composite dilations. This framework extends the traditional wavelet approach by allowing for waveforms to be defined not only at various scales and locations but also according to various orthogonal transformations such as shearing transformations. The shearlet representation is, perhaps, the most widely known example of wavelets with composite dilations. However, many other representations are obtained within this framework, where directionality properties are controlled by different types of orthogonal matrices, such as the newly defined hyperbolets. In this paper, we show how to take advantage of different wavelets with composite dilations to sparsely represent important features such as edges and texture independently, and apply these techniques to derive improved algorithms for image denoising

Searchlight CT: A new reconstruction method for collimated X-ray tomography

The method presented in this paper aims to reduce the overall radiation exposure from X-ray CT scans when only the reconstruction of a region of interest is required. To achieve this goal, the Searchlight CT algorithm restricts the acquisition to X-rays passing mainly through the region of interest. The algorithm uses an iteration of the X-ray transform and of a regularized inverse, which converges rapidly and for which generic conditions of converges are provided. The performance of the Searchlight CT algorithm is illustrated on both phantom and experimental data

Functional vs Structural Cortical Deficit Pattern Biomarkers for Major Depressive Disorder

Importance: Major depressive disorder (MDD) is a severe mental illness characterized more by functional rather than structural brain abnormalities. The pattern of regional homogeneity (ReHo) deficits in MDD may relate to underlying regional hypoperfusion. Capturing this functional deficit pattern provides a brain pattern-based biomarker for MDD that is linked to the underlying pathophysiology. Objective: To examine whether cortical ReHo patterns provide a replicable biomarker for MDD that is more sensitive than reduced cortical thickness and evaluate whether the ReHo MDD deficit pattern reflects regional cerebral blood flow (RCBF) deficit patterns in MDD and whether a regional vulnerability index (RVI) thus constructed may provide a concise brain pattern-based biomarker for MDD. Design, settings, and participants: The UK Biobank (UKBB) participants had ReHo and structural measurements. Participants from the Enhancing Neuroimaging Genetics Through Meta-Analysis (ENIGMA) Consortium were included for measuring the MDD structural cortical deficit pattern. The UKBB ReHo and ENIGMA cortical thickness effect sizes for MDD were used to test the deficit patterns in the Amish Connectome Project (ACP) with ReHo, structural, and RCBF data. Finally, the Ament Clinic Inc (ACI) sample had RCBF data measured using single-photon emission computed tomography. Data were analyzed from August 2021 to September 2024. Exposures: ReHo and structural measurements. Results: Included in this analysis were 4 datasets: (1) UKBB (N = 4810 participants; 2220 with recurrent MDD and 2590 controls; mean [SD] age, 63.0 [7.5] years; 1121 female [50%]), (2) ENIGMA (N = 10 115 participants; 2148 with MDD and 7957 healthy controls; mean [SD] age, 39.9 [10.0] years; 5927 female [59%]), (3) ACP (N = 204 participants; 68 with a lifetime diagnosis of MDD and 136 controls; mean [SD] age, 41.0 [14.5] years; 104 female [51%]), and (4) ACI (N = 372 participants; 296 with recurrent MDD and 76 controls; mean [SD] age, 45.3 [17.2] years; 189 female [51%]). MDD participants had lower cortical ReHo in the cingulum, superior temporal lobe, frontal lobe, and several other areas, with no significant differences in cortical thickness. The regional pattern of ReHo MDD effect sizes was significantly correlated with that of RCBF obtained from 2 independent datasets (Pearson r = 0.52 and Pearson r = 0.46; P \u3c 10-4). ReHo and RCBF functional RVIs showed numerically stronger effect sizes (Cohen d = 0.33-0.90) compared with structural RVIs (Cohen d = 0.09-0.20). Elevated ReHo-based RVI-MDD values in individuals with MDD were associated with higher depression symptom severity across cohorts. Conclusions and relevance: Results of this case-control study suggest that the ReHo MDD deficit pattern reflected cortical hypoperfusion and was regionally specific in MDD. ReHo-based RVI may serve as a sensitive functional biomarker for MDD

Improved Automatic Centerline Tracing for Dendritic and Axonal Structures

Centerline tracing in dendritic structures acquired from confocal images of neurons is an essential tool for the construction of geometrical representations of a neuronal network from its coarse scale up to its fine scale structures. In this paper, we propose an algorithm for centerline extraction that is both highly accurate and computationally efficient. The main novelties of the proposed method are (1) the use of a small set of Multiscale Isotropic Laplacian filters, acting as self-steerable filters, for a quick and efficient binary segmentation of dendritic arbors and axons; (2) an automated centerline seed points detection method based on the application of a simple 3D finite-length filter. The performance of this algorithm, which is validated on data from the DIADEM set appears to be very competitive when compared with other state-of-the-art algorithms.National Science Foundation/[1320910]/NSF-DMS/Estados UnidosNational Science Foundation/[1008900]/NSF-DMS/Estados UnidosNational Science Foundation/[1005799]/NSF-DMS/Estados UnidosNorman Hackerman Advanced Research Program/[003652-0136-2009]/NHARP/Estados UnidosUCR::Vicerrectoría de Docencia::Ciencias Básicas::Facultad de Ciencias::Escuela de Matemátic