Abstract
To recover a signal from its linear measurements, the present paper considers the relaxed analysis LASSO (RALASSO) optimization model. An algorithm involving a gradient descent operator and a soft shrinkage operator in each iteration is proposed to solve RALASSO, termed iterative gradient descent shrinkage (IGDS). Further, being not restricted to the sparsity regime, we replace the ℓ1-norm regularizer in RALASSO by a general regularization function, and derive an algorithm framework for solving this more general problem. The framework employs a denoiser as a black-box to replace the soft shrinkage operator, thus we call it iterative gradient descent denoising (IGDD). IGDS can be viewed as a special instance of IGDD. The recovery performance of IGDD armed with a good denoiser will be better than that of IGDS. Extensive experimental results based on several numerical examples and image restoration tasks show that our algorithms have advantages over some analysis-model-based algorithms and denoiser-based ones, in terms of recovery capability or run-time.
Published Version
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