Two efficient models in two-dimensional signal processing are proposed in the thesis. The first model deals with large scale spectral compressive sensing in continuous domain, which aims to recover a 2D spectrally sparse signal from partially observed time samples. The signal is assumed to be a superposition of s complex sinusoids. We propose a semidefinite program for the 2D signal recovery problem. Our model is able to handle large scale 2D signals of size 500*500, whereas traditional approaches only handle signals of size around 20*20. The second model deals with the problem of single image reflection suppression. Removing the undesired reflection from images taken through glass is of great importance in computer vision. It serves as a means to enhance the image quality for aesthetic purposes as well as to preprocess images in machine learning and pattern recognition applications. We propose a convex model to suppress the reflection from a single input image. Our model implies a partial differential equation with gradient thresholding, which is solved efficiently using Discrete Cosine Transform. Extensive experiments on synthetic and real-world images demonstrate that our approach achieves desirable reflection suppression results and dramatically reduces the execution time compared to the state of the art.