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Coordination Number and Geometry

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For transition metal complexes, the coordination number determines the geometry around the central metal ion. Table 1 compares coordination numbers to molecular geometry. The most common structures of the complexes in coordination compounds are octahedral, tetrahedral, and square planar.

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Related Experiment Video

Updated: Jan 19, 2026

Studying Visual Awareness and Motion-Induced Blindness

Studying Visual Awareness and Motion-Induced Blindness

Published on: April 30, 2023

On the Global Geometry of Sphere-Constrained Sparse Blind Deconvolution.

Yuqian Zhang, Yenson Lau, Han-Wen Kuo

IEEE Transactions on Pattern Analysis and Machine Intelligence

|September 9, 2019

Summary

This study introduces a novel two-stage algorithm for sparse blind deconvolution, effectively recovering signals from blurred images. The method leverages spherical constraints to overcome ill-posedness in blind deconvolution problems.

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Last Updated: Jan 19, 2026

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Area of Science:

Signal Processing
Optimization
Computational Imaging

Background:

Blind deconvolution is an ill-posed problem requiring additional constraints or priors.
Existing methods struggle with sparse and randomly populated activation signals.

Purpose of the Study:

To develop an effective algorithm for sparse blind deconvolution under spherical constraints.
To address the challenges of recovering activation signals and convolutional kernels from their convolution.

Main Methods:

Formulating sparse blind deconvolution as a nonconvex optimization problem over a sphere.
Normalizing the convolution kernel to have unit Frobenius norm.
Developing a two-stage algorithm leveraging properties of local minima on the sphere.

Main Results:

Demonstrating that spurious local minima are close to signed shift truncations of the ground truth.
Successfully recovering ground truth signals in microscopy and image deblurring applications.
Showing promising performance in challenging image deblurring scenarios.

Conclusions:

The proposed geometry-inspired algorithm effectively solves sparse blind deconvolution.
The insights and algorithm extend to convolutional dictionary learning.
The method offers a robust approach for signal recovery in various imaging applications.