Sparsity‐aware adaptive block‐based compressive sensing

Abstract

Recently, multidimensional signal reconstruction using a low number of measurements is of great interest. Therefore, an effective sampling scheme which should acquire the most information of signal using a low number of measurements is required. In this paper, we study a novel cube-based method for sampling and reconstruction of multidimensional signals. First, inspired by the block-based compressive sensing (BCS), we divide a group of pictures (GoP) in a video sequence into cubes. By this way, we can easily store the measurement matrix and also easily can generate the sparsifying basis. The reconstruction process also can be done in parallel. Second, along with the Kronecker structure of the sampling matrix, we design a weight matrix based on the human visuality system, i.e. perceptually. We will also benefit from different weighted ℓ1-minimization methods for reconstruction. Furthermore, conventional methods for BCS 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. Motivated by this point, we will adaptively allocate the samples for each cube in a video sequence. Our aim is to show that our simple linear sampling approach can be competitive with the other state-of-the-art methods.

Multilevel magnetic resonance imaging compression using compressive sensing

“…The results in Table 4 show that the proposed algorithm outperforms the algorithm in [19] for all six images, with an average PSNR gain of 2.22 dB. It is worth mentioning here that the algorithm in [19] is not suggested to compress MRI images, while the proposed algorithm in this paper is designed to compress only MRI images.…”

“…The results of the proposed algorithm in this paper are also compared with the results of the algorithm presented in [19]. To achieve a fair comparison, the six MRI images used in this paper are compressed using the algorithm proposed with numerical sparsity in [19]. Table 4 shows the PSNR values for the same CL value for each MRI image.…”

“…The proposed formula here quantises the histogram of the SI values into four levels. Some other formulas are suggested in the literature that uses numerical sparsity as in [19].…”

“…Razzaq et al in [17, 18] present non‐uniform sparsity constraints method, which transforms the whole MRI image into the frequency domain, then splits the image in the sparse domain into five parts according to their sparsity levels. An adaptive sparsity block‐based CS is proposed in [19], this paper suggests two methods to choose the number of samples allocated for each block, based on the sparsity of signal in the DCT domain.…”

Adaptive gradient-based block compressive sensing with sparsity for noisy images

“…They used certain block partitions and the block size ranged from 4 to 90. Both [42] and [48] proposed an adaptive block-based compressive sensing approach which collected a different number of samples of the measurement matrix for each block. [9] studied block compressive sensing in wireless sensor networks and [3] analyzed the block sampling strategies in compressive sensing.…”