Block-based compressed sensing has been a popular topic in image compression researches. A major portion of papers with this topic concentrates on compression performances based on rate-distortion theory. Here, we focus on the performances of reconstructed images with the transmission over lossless and lossy channels. Conventional block-based compressed sensing chooses fixed-sized square blocks to perform encoding. With quadtree partition that is based on the characteristics of image regions, we can separate square blocks with different sizes, and then perform compressed sensing independently. By fixing the measurement rate in both cases, we can observe and compare the performances with fixed-sized blocks and those with quadtree partition with the different percentages of block sizes. Better performances with quadtree partition can be observed in most cases.