A key requirement for network management is the accurate and reliable monitoring of relevant network characteristics. In today's large-scale networks, this is a challenging task due to the scarcity of network measurement resources and the hard constraints that this imposes. This paper proposes a new framework, called SNIPER, which leverages the flexibility provided by Software-Defined Networking (SDN) to design the optimal observation or measurement matrix that can lead to the best achievable estimation accuracy using Matrix Completion (MC) techniques. To cope with the complexity of designing large-scale optimal observation matrices, we use the Evolutionary Optimization Algorithms (EOA) which directly target the ultimate estimation accuracy as the optimization objective function. We evaluate the performance of SNIPER using both synthetic and real network measurement traces from different network topologies and by considering two main applications for per-flow size and delay estimations. Our results show that SNIPER can be applied to a variety of network performance measurements under hard resource constraints. For example, by measuring only 8.8% of all per-flow path delays in Harvard network [1], congested paths can be detected with probability of 0.94. To demonstrate the feasibility of our framework, we also have implemented a prototype of SNIPER in Mininet.