Deep neural networks have substantially improved reconstruction performance for compressive sensing (CS) in comparison to traditional optimization algorithms. However, their vulnerability to noise remains a critical challenge, often leading to significant degradation in performance. To overcome this challenge, we propose a universal algorithm that introduces orthogonality constraints on both the learned measurement matrix and the reconstruction neural network model in CS, with the objective of enhancing the resilience to noise for existing learning-based CS methods while preserving high reconstruction performance. To be concrete, we first develop an approximate restricted isometry property (RIP) to optimize the learned measurement matrix, thereby ensuring stable sampling in accordance with CS theory. We demonstrate that the approximate RIP is equivalent to imposing orthogonality constraints on the measurement matrix. Subsequently, we extend these orthogonality constraints to the reconstruction network to guarantee robust recovery with theoretical guarantees. Comprehensive experimental evaluations demonstrate that our approach significantly enhances robustness of learning-based CS methods, achieving competitive reconstruction performance when compared to current CS approaches.