Moving Least Squares Algorithm for Deforming Points and Images-MATLAB Implementation

This resource demonstrates the use of Least Squares Method to fit a circle curve. The output includes the coordinates of the center and the radius of the fitted circle.

针对一组x，y值的基于最小平方方差和的椭圆和圆的拟合，用Matlab实现。

本工具箱内含有MATLAB解决非线性最小二乘优化问题的所有m函数文件代码，方便用户高效地实现相关计算与优化。

在圆拟合的过程中，直接最小二乘法是用于代数曲面拟合的重要技术。通过将数据点最小化到拟合曲面的距离，可以实现高效、精确的曲面拟合。

Total variation regularized least squares deconvolution is one of the standard problems in image processing. This package uses the concept of Augmented Lagrangian [1] to implement the state-of-the-art algorithm, which can be viewed as a variant of the widely known Alternating Direction Method of Multipliers (ADMM). The deconvtv user interface is similar to the current MATLAB deconvolution tools, including deconvwnr, deconvlucy, and deconvreg: out = deconvtv(img, psf, mu, opt); deconvtv supports direct spatiotemporal processing for image and video deconvolution problems. Its applications include, but are not limited to: image and video deblurring, image and video denoising, depth data enhancement, thermal air turbulence stabilization, and multi-view synthesis. For more information and citations, please refer to: [1] SH Chan, R. Khoshabeh, KB Gibson, PE Gill, and TQ Nguyen, \"Augmented Lagrangian Method for Total Variation Video Restoration\", IEEE Trans. Image.

在[-1,1]区间上取n=20个等距节点，计算出以相应节点上的e^x的值作为数据样本，以1，x，x²，⋯，x^l为基函数做出l=3,5,7,9次的最小二乘拟合多项式。画出ln(cond(A)) - l曲线，其中A是确定最小二乘多项式系数的矩阵。计算出不同阶最小二乘多项式给出的最小偏差σ(l)。将基函数改为1，P₁(x)，P₂(x)，⋯，Pₗ(x)，其中Pᵢ(x)是勒让德多项式，结果如何？

本论文针对BP算法，即当前前馈神经网络训练中应用最多的算法进行改进，并在MATLAB中实现。

Golden Section Search Algorithm Overview of the Algorithm The Golden Section Search algorithm is an optimization technique used to find the extremum (maximum or minimum) of a unimodal function within a specified interval. It leverages the golden ratio to reduce the search interval step-by-step, ensuring efficient convergence. Steps of the Algorithm Initialize two points within the interval [a, b] using the golden ratio. Evaluate the function at these two points. Compare the function values and update the interval by removing the unnecessary part. Repeat the process until the desired precision is reached. Return the optimal point and function value. MATLAB Implementation Below is a sample MATLAB code to implement the Golden Section Search algorithm: function [x_opt, f_opt] = golden_section_search(f, a, b, tol) phi = (1 + sqrt(5)) / 2; c = b - (b - a) / phi; d = a + (b - a) / phi; while abs(b - a) > tol if f(c) < f xss=removed xss=removed xss=removed xss=removed xss=removed xss=removed> This code defines a function golden_section_search that finds the optimal point within the interval [a, b] using Golden Section Search. Advantages Efficient for unimodal functions. Simple to implement with minimal function evaluations. Converges faster than other search methods for specific cases.

利用MATLAB代码对OFDM的同步算法进行仿真，采用短训练序列的互相关运算进行帧同步，并利用长训练序列的互相关实现符号同步。