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[Your Name/Organization] Date: October 2023 Abstract Linear inverse problems are ubiquitous in fields ranging from medical imaging to geophysics and astronomy. Solving these problems—often formulated as large-scale linear systems $Ax=b$—requires sophisticated numerical methods to handle ill-posedness, noise, and computational complexity. We introduce RESTORETOOLS , a Julia package designed to provide a unified, high-performance framework for the restoration and solution of linear systems. RESTORETOOLS implements state-of-the-art iterative algorithms, including Krylov subspace methods and hybrid approaches, with a specific focus on handling matrix-free operators and efficient regularization. This paper details the mathematical underpinnings, software architecture, and practical application of the package, demonstrating its efficacy in solving large-scale restoration problems with superior performance compared to traditional scripting approaches. 1. Introduction The problem of "restoration" generally refers to the recovery of an original signal or image from observed data that has been degraded by a linear process and noise. Mathematically, this is expressed as: Sone385engsub+convert020002+min+verified Here
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