Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In one-bit compressed sensing (1-bit CS), one attempts to estimate a structured parameter (signal) only using the sign of suitable linear measurements. ,  investigate 1-bit CS problems for sparse signals using the recently proposed k-support norm.  show that the new estimator has a closed-form solution, so no optimization is needed.  establish consistency and recovery guarantees of the estimator for both Gaussian and subGaussian random measurements. For Gaussian measurements, our estimator is comparable to the best known in the literature, along with guarantees on support recovery. For sub-Gaussian measurements, our estimator has an irreducible error which, unlike existing results, can be controlled by scaling the measurement vectors. In both cases, our analysis covers the setting of model misspecification, i.e., when the true sparsity is unknown. Experimental results illustrate several strengths of the new estimator.
['Sheng Chen', 'Arindam Banerjee']
I am writing a research paper on a idea One-bit Compressed Sensing with the k-Support Norm
[{"from": "human", "value": "I am writing a research paper on a idea One-bit Compressed Sensing with the k-Support Norm"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In one-bit compressed sensing (1-bit CS), one attempts to estimate a structured parameter (signal) only using the sign of suitable linear measurements. ,  investigate 1-bit CS problems for sparse signals using the recently proposed k-support norm.  show that the new estimator has a closed-form solution, so no optimization is needed.  establish consistency and recovery guarantees of the estimator for both Gaussian and subGaussian random measurements. For Gaussian measurements, our estimator is comparable to the best known in the literature, along with guarantees on support recovery. For sub-Gaussian measurements, our estimator has an irreducible error which, unlike existing results, can be controlled by scaling the measurement vectors. In both cases, our analysis covers the setting of model misspecification, i.e., when the true sparsity is unknown. Experimental results illustrate several strengths of the new estimator."}]