ORKA: Object reconstruction using a K-approximation graph

TL;DR

This paper introduces ORKA, a novel object reconstruction method using a K-approximation graph that effectively handles incomplete and noisy data by exploiting structured sparsity and object continuity across measurements.

Contribution

It proposes a new model for object data assuming sparsity and continuity, along with an efficient algorithm and proven approximation bounds for reconstruction.

Findings

Effective reconstruction in noisy, incomplete data scenarios

Optimal approximation bounds established

Successful application examples in geophysics and video processing

Abstract

Data processing has to deal with many practical difficulties. Data is often corrupted by artifacts or noise and acquiring data can be expensive and difficult. Thus, the given data is often incomplete and inaccurate. To overcome these problems, it is often assumed that the data is sparse or low-dimensional in some domain. When multiple measurements are taken, this sparsity often appears in a structured manner. We propose a new model that assumes the data only contains a few relevant objects, i.e., it is sparse in some object domain. We model an object as a structure that can only change slightly in form and continuously in position over different measurements. This can be modeled by a matrix with highly correlated columns and a column shift operator that we introduce in this work. We present an efficient algorithm to solve the object reconstruction problem based on a K-approximation graph. We prove optimal approximation bounds and perform a numerical evaluation of the method. Examples from applications including Geophysics, video processing, and others will be given.