SIAM Undergraduate Research Online
Volume 11
In This Volume
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Median Filtering by Threshold Decomposition: Induction Proof
Published electronically December 19, 2018DOI: 10.1137/18S017120
Authors
Connor Bramham (Socrates Prep), Brandon Mayle (Socrates Prep), Maura Gallagher (Socrates Prep), Douglas Magruder (Socrates Prep), Cooper Reep (Socrates Prep)
Project Advisors
Neal Gallagher (Socrates Prep)
Abstract
In building a robot for the FTC competition, our team needed to remove motor noise from our sensor signals. So we settled on using a median filter because of the medians superior removal of impulsive noise. For us, however, the foundational publications that describe these filters were challenging to understand. Having learned the concept of proof by induction from the MIT OpenCourseWare course, “Mathematics for Computer Science” (MIT Course Number 6.042J / 18.062J), we developed an original proof for the principle of median filter threshold decomposition in order to better understand their operation. The induction is over the number of quantized threshold levels for the sequence of input values as applied to both the standard and recursive median filter.
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A spectral element method for meshes with skinny elements
Published electronically December 6, 2018 -
Optimal Net Energy and Foraging Behavior of Grus americana in Aransas National Wildlife Refuge
Published electronically November 30, 2018 -
Using a Density Dependent Population Model to Examine Sperm Whale Population Dynamics in the Gulf of Mexico Before and After an Environmental Disturbance
Published electronically November 30, 2018 -
Comparing Language Use and Network Structure Using Twitter
Published electronically November 26, 2018 -
Convergence of the Randomized Block Gauss-Seidel Method
Published electronically November 8, 2018 -
Forecasting Algal Bloom Lags and Stability in a Watershed
Published electronically October 10, 2018 -
Better ATE Than Never: A Mathematical Analysis of Food Waste Production and Redistribution
Published electronically September 27, 2018 -
Using Data Assimilation to Better Predict Contaminant Transport in Fluids
Published electronically September 20, 2018 -
A Multi-Dam System Design for Zambezi River
Published electronically September 6, 2018 -
Toxoplasma gondii: A mathematical model of its transfer between cats and the environment
Published electronically August 29, 2018 -
A Robust Optimization Approach for Selecting Urban Fire Engine Company Locations
Published electronically August 20, 2018 -
Resilient Jammed Packing: A Novel Feature of a Classic Geometry Problem
Published electronically June 26, 2018 -
Implementation of Gibbs Sampling within Bayesian Inference and its Applications in Actuarial Science
Published electronically June 13, 2018 -
Wronskian representations of hypergeometric integrals
Published electronically June 7, 2018 -
Investigating the Gerchberg-Saxton Phase Retrieval Algorithm
Published electronically May 2, 2018 -
Linear Extensions of a Partial Order Subject to Algebraic Constraints
Published electronically March 28, 2018 -
Increasing Efficiency for United Way's Free Tax Campaign
Published electronically March 23, 2018 -
Calibration of the Ross Recovery Theorem to Real-world Data, and Tests of its Practical Value
Published electronically March 19, 2018 -
A Two-Stage Vehicle Routing Algorithm Applied to Disaster Relief Logistics after the 2015 Nepal Earthquake
Published electronically March 15, 2018 -
L1 Regularization for Compact Support
Published electronically March 14, 2018 -
Exploring Blood Flow Dynamics Underlying Pathogenesis of Splenic Artery Aneurysms
Published electronically March 5, 2018 -
An Alternating Minimization Method to Train Neural Network Models for Brain Wave Classification
Published electronically February 21, 2018 -
Modeling Tsunami Run-Up and Draw-Down on the Beach
Published electronically February 21, 2018 -
Rank and Score Aggregation Methods in Competitive Climbing
Published electronically January 24, 2018 -
A Generalization of the Minisum and Minimax Voting Methods
Published electronically January 23, 2018 -
An Analysis of the Impact of Self-Driving Cars on Traffic Conditions
Published electronically January 19, 2018
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