Guided Signal Reconstruction with Application to Image Magnification

TL;DR

This paper introduces a new signal reconstruction method using guiding subspaces and iterative algorithms, significantly improving image magnification quality over existing schemes.

Contribution

It presents a novel convex set-based framework and conjugate gradient algorithms for optimal signal reconstruction with applications to image magnification.

Findings

Reconstructed images surpass traditional methods in quality.

The algorithms are computationally efficient and low-memory.

The approach effectively utilizes guiding subspaces for better reconstruction.

Abstract

We study the problem of reconstructing a signal from its projection on a subspace. The proposed signal reconstruction algorithms utilize a guiding subspace that represents desired properties of reconstructed signals. We show that optimal reconstructed signals belong to a convex bounded set, called the "reconstruction" set. We also develop iterative algorithms, based on conjugate gradient methods, to approximate optimal reconstructions with low memory and computational costs. The effectiveness of the proposed approach is demonstrated for image magnification, where the reconstructed image quality is shown to exceed that of consistent and generalized reconstruction schemes.