Projects

Various Small Projects on Various Subjects.

Calculate Distance Matrix

Implementation for calculation of the distance matrix between 2 sets of vectors.

Clustering

Some implementations of Clustering algorithms.

Deep Learning Matched Filter

Analyze the Matched Filter performance using Deep Learning.
Mainly if it could have better performance compared to Matched Filter in low SNR.
Project in Progress...

Dynamic Time Warping

Introduction and implementation of the Dynamic Time Warping concept.

Image Convolution

Implementation of Image Convolution using Multi Threading and SIMD (Vectrorization) for speed. The project generates DLL / DYLIB / SO to be used in MATLAB.

Image Bilateral Filter

Implementation of the Bilateral Filter for Image Processing.

Image to Columns

Optimized C based implementation of MATLAB's im2col() function.

Levinson Recursion

Implementation of the Levinson Recursion on MATLAB.
This allows solving Linear System A x = b where A is a Toeplitz Matrix in O(N^2) complexity instead of O(N^3) using classic solution.

Localization

Simulation of Localization Methods.
Deriving DTOA / TDOA Localization Cramer Rao Lower Bound.

Optimization

Various projects which are Optimization (Numerical Methods) oriented such as:

• Projection into Balls (Like Norm Balls, the Simplex Ball, etc...).
• Interior Point () - Implementation in MATLAB.
• Steepest Descent - Calculation of the Steepest Descent Direction for various norms ($ {L}{1} $, $ {L}{2} $, $ {L}_{\infty} $).

Singular Value Decomposition

A Presentation about Singular Value Decomposition (SVD).
It covers the following:

• Singular Value Theorem.
• Applications
  • Dimensionality Reduction.
  • Solving Linear Equation System (Least Squares).
  • Total Least Squares.
  • Principal Component Analysis (PCA).

The PDF can be viewed directly - SVD Presentation PDF.

SLEEF vs. SVML

Comparison (Run Time Benchmark) of SLEEF vs. SVML for various numerical functions.

Task Assignment Problem

Analysis of a variation of the Knapsack Problem.

To Do

• Exploratory Principal Component Analysis.
  Implement in MATLAB.