DeepAI AI Chat
Log In Sign Up

Algorithms for Piecewise Constant Signal Approximations

by   Leif Bergerhoff, et al.

We consider the problem of finding optimal piecewise constant approximations of one-dimensional signals. These approximations should consist of a specified number of segments (samples) and minimise the mean squared error to the original signal. We formalise this goal as a discrete nonconvex optimisation problem, for which we study two algorithms. First we reformulate a recent adaptive sampling method by Dar and Bruckstein in a compact and transparent way. This allows us to analyse its limitations when it comes to violations of its three key assumptions: signal smoothness, local linearity, and error balancing. As a remedy, we propose a direct optimisation approach which does not rely on any of these assumptions and employs a particle swarm optimisation algorithm. Our experiments show that for nonsmooth signals or low sample numbers, the direct optimisation approach offers substantial qualitative advantages over the Dar--Bruckstein method. As a more general contribution, we disprove the optimality of the principle of error balancing for optimising data in the l^2 norm.


page 1

page 2

page 3

page 4


Image segmentation by optimal and hierarchical piecewise constant approximations

Piecewise constant image approximations of sequential number of segments...

Piecewise Approximations of Black Box Models for Model Interpretation

Machine Learning models have proved extremely successful for a wide vari...

Monte Carlo twisting for particle filters

We consider the problem of designing efficient particle filters for twis...

Stable Segmentation of Digital Image

In the paper the optimal image segmentation by means of piecewise consta...

Analysis and Optimisation of Bellman Residual Errors with Neural Function Approximation

Recent development of Deep Reinforcement Learning has demonstrated super...

Adaptive Stochastic Optimisation of Nonconvex Composite Objectives

In this paper, we propose and analyse a family of generalised stochastic...