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You can employ Compressed Sensing / Sparse Representation for Super Resolution in Frequency Domain. One way to do so is solving the problem: $$ \arg \min_{\boldsymbol{x}} \frac{1}{2} {\left\| F \boldsymbol{x} - \boldsymbol{y} \right\|}_{2}^{2} + \lambda {\left\| \boldsymbol{x} \right\|}_{1} $$ Where the $ {L}_{1} $ norm is sparsity inducing regularization ...


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This question is typically the subject of a paper like Robust Uncertainty Principles: Exact Signal Reconstruction From Highly Incomplete Frequency Information, Emmanuel J. Cand├Ęs, Justin Romberg, 2006: This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discrete-time signal $f\in \mathbb{C}^N$ and ...


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