A General Rate-Distortion Optimization Method for Block Compressed Sensing of Images

Block compressed sensing (BCS) is a promising technology for image sampling and compression for resource-constrained applications, but it needs to balance the sampling rate and quantization bit-depth for a bit-rate constraint. In this paper, we summarize the commonly used CS quantization frameworks into a unified framework, and a new bit-rate model and a model of the optimal bit-depth are proposed for the unified CS framework. The proposed bit-rate model reveals the relationship between the bit-rate, sampling rate, and bit-depth based on the information entropy of generalized Gaussian distribution. The optimal bit-depth model can predict the optimal bit-depth of CS measurements at a given bit-rate. Then, we propose a general algorithm for choosing sampling rate and bit-depth based on the proposed models. Experimental results show that the proposed algorithm achieves near-optimal rate-distortion performance for the uniform quantization framework and predictive quantization framework in BCS.

Image Encryption Scheme Based on Multiscale Block Compressed Sensing and Markov Model

Many image encryption schemes based on compressed sensing have the problem of poor quality of decrypted images. To deal with this problem, this paper develops an image encryption scheme by multiscale block compressed sensing. The image is decomposed by a three-level wavelet transform, and the sampling rates of coefficient matrices at all levels are calculated according to multiscale block compressed sensing theory and the given compression ratio. The first round of permutation is performed on the internal elements of the coefficient matrices at all levels. Then the coefficient matrix is compressed and combined. The second round of permutation is performed on the combined matrix based on the state transition matrix. Independent diffusion and forward-backward diffusion between pixels are used to obtain the final cipher image. Different sampling rates are set by considering the difference of information between an image’s low- and high-frequency parts. Therefore, the reconstruction quality of the decrypted image is better than that of other schemes, which set one sampling rate on an entire image. The proposed scheme takes full advantage of the randomness of the Markov model and shows an excellent encryption effect to resist various attacks.

Multitrack Compressed Sensing for Faster Hyperspectral Imaging

Hyperspectral imaging (HSI) provides additional information compared to regular color imaging, making it valuable in areas such as biomedicine, materials inspection and food safety. However, HSI is challenging because of the large amount of data and long measurement times involved. Compressed sensing (CS) approaches to HSI address this, albeit subject to tradeoffs between image reconstruction accuracy, time and generalizability to different types of scenes. Here, we develop improved CS approaches for HSI, based on parallelized multitrack acquisition of multiple spectra per shot. The multitrack architecture can be paired up with either of the two compatible CS algorithms developed here: (1) a sparse recovery algorithm based on block compressed sensing and (2) an adaptive CS algorithm based on sampling in the wavelet domain. As a result, the measurement speed can be drastically increased while maintaining reconstruction speed and accuracy. The methods were validated computationally both in noiseless as well as noisy simulated measurements. Multitrack adaptive CS has a ∼10 times shorter measurement plus reconstruction time as compared to full sampling HSI without compromising reconstruction accuracy across the sample images tested. Multitrack non-adaptive CS (sparse recovery) is most robust against Poisson noise at the expense of longer reconstruction times.

Modified Block Compressed Sensing for Extraction of Fetal Electrocardiogram from Mother Electrocardiogram Using Block Compressed Sensing Based Guided FOCUSS and FAST-Independent Component

Fetal ECG extraction from abdominal ECG is critical task for telemonitoring of fetus which require lot of understanding to the subject. Conventional source separation methods are not efficient enough to separate FECG from huge multichannel ECG. Thus use of compression technique is needed to compress and reconstruct ECG signal without any significant losses in quality of signal. Compressed sensing shows promising results for such tasks. However, current compressed sensing theory is not so far that successful due to the non-sparsity and strong noise contamination present in ECG signal. The proposed work explores the concept of block compressed sensing to reconstruct non-sparse FECG signal using GFOCUSS algorithm. The main objective of this paper is not only to successfully reconstruct the ECG signal but to efficiently separate FECG from abdominal ECG. The proposed algorithm is explained in very extensive manner for all experiments. The key feature of proposed method is, that it doesn’t affect the interdependence relation between multichannel ECG. The useof walsh sensing matrix made it possible to achieve high compression ratio. Experimental results shows that even at very high compression ratio, successful FECG reconstruction from raw ECG is possible. These results are validated using PSNR, SINR, and MSE. This shows the framework, compared to other algorithms such as current blocking CS algorithms, rackness CS algorithm and wavelet algorithms, can greatly reduce code execution time during data compression stage and achieve better reconstruction in terms of MSE, PSNR and SINR.