A structured RMIL conjugate gradient-based strategy for nonlinear least squares with applications in image restoration problems

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Abstract
Numerous scientific and technical domains have found use for nonlinear least squares (NLS). Conventional approaches to NLS problem solving often suffer from computational inefficiencies and high memory requirements, particularly when applied to large-scale systems. This paper presents the structured conjugate gradient coefficient using a structured secant-like approximation to solve NLS problems. The approach develops a structured vector approximation that captures the vector-matrix relationship using Taylor series expansions of the Hessian of the goal function. It is possible to incorporate more Hessian information into the traditional search direction, since this approximation satisfies a quasi-Newton condition. Furthermore, given conventional assumptions, a global convergence study is performed. Benchmark NLS tasks are used for numerical studies to assess the method's performance against alternative approaches. The results demonstrate the promise and success of the approach. Lastly, problems with image restoration are addressed using the suggested technique.

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