Conventional methods for block‐based compressive sensing consider an equal number of samples for all blocks. However, the sparsity order of blocks in natural images could be different and, therefore, a various number of samples could be required for their reconstruction. In this study, the authors propose an adaptive block‐based compressive sensing scheme, which collects a different number of samples from each block. The authors show that by adapting the sampling rate, in addition to reducing the whole required number of measurements, the reconstruction performance would be improved, simultaneously. Simulation results verify the effectiveness of the proposed scheme, especially for multi‐level pixel value images like Mondrian test image.

In this study, the authors propose a distributed form of Kalman filter for non‐linear dynamics as a generalised Kalman consensus filter (GKCF) and prove its stability, analytically. More specifically, the authors obtain the sufficient condition for asymptotical convergence using Lyapunov analysis. For this purpose, the authors propose four lemmas and show that Kalman consensus filter (KCF) in a linear system is a special case of the authors’ proposed GKCF.