Compressive sensed video recovery via iterative thresholding with random transforms

Abstract

We consider the problem of compressive sensed video recovery via iterative thresholding algorithm. Traditionally, it is assumed that some fixed sparsifying transform is applied at each iteration of the algorithm. In order to improve the recovery performance, at each iteration the thresholding could be applied for different transforms in order to obtain several estimates for each pixel. Then the resulting pixel value is computed based on obtained estimates using simple averaging. However, calculation of the estimates leads to significant increase in reconstruction complexity. Therefore, we propose a heuristic approach, where at each iteration only one transform is randomly selected from some set of transforms. First, we present a simple example, when block-based 2-D discrete cosine transform is used as the sparsifying transform, and show that the random selection of the block size at each iteration significantly outperforms the case when fixed block size is used. Then, we show that similar improvement can be achieved, when a random shift of the blocks grid is introduced, or when random 2-D discrete wavelet transform is applied at each iteration. Second, building on these simple examples, we apply the proposed approach when video block-matching and 3D filtering (VBM3D) is used for the thresholding and show that the recovery performance could be improved as compared with the recovery based on VBM3D with fixed transform. Finally, extending the introduced approach, we propose to also randomly select a frame residual computation algorithm as well and show that it could provide additional gain as well.

Multi-Image Compression–Encryption Algorithm Based on Compressed Sensing and Optical Encryption

“…Compressed sensing is a new signal sampling compression theory, which can realize image compression and encryption simultaneously during the sampling period [ 4 , 5 ]. Two-dimensional compressed sensing is to sample and measure the signal from two directions, which can not only further reduce the size of the compressed image, but also make the reconstructed image obtain better reconstruction quality.…”

“…Since CS was proposed, many compression and encryption algorithms based on CS have appeared. Belyaev et al [ 5 ] studied an iterative threshold-based compressed sensing video restoration algorithm. Huang et al [ 6 ] embedded the encrypted image into the carrier image after SHA-3 and CS compression to achieve multi-image visual security.…”

An Efficient Compressive Sensed Video Codec with Inter-Frame Decoding and Low-Complexity Intra-Frame Encoding

“…The main contributions of this paper are the following: We introduce an accurate rate control algorithm based on packet dropping which does not lead to a noticeable increase in encoding complexity. We propose fast randomized thresholding for the ISTA, which pseudo-randomly selects the shrinkage parameters at each iteration and shows that compared with the ISTA with VBM3D [ 22 , 23 ], it is significantly less complex and provides better recovery performance. We show detailed comparisons of the proposed CS-JPEG codec with conventional optimized competitors, such as MJPEG, x264 (Intra), and x265 (Intra) [ 24 ] (fast software implementation of H.265/HEVC [ 25 ]) in ultrafast profiles.…”

“…We propose fast randomized thresholding for the ISTA, which pseudo-randomly selects the shrinkage parameters at each iteration and shows that compared with the ISTA with VBM3D [ 22 , 23 ], it is significantly less complex and provides better recovery performance.…”

An Adaptive Rate Blocked Compressive Sensing Method for Video

“…According to measurement models, CS methods can be divided into ones using global measurement scheme [11] and some others using block compressive sensing scheme (BCS) [12,13]. In general, global measurement methods can get better performance in the non-adaptive case [14]. However, the size of the measurement matrices in global measurement methods are often very large, so the total number of matrix multiplication in the sampling process will be large, and memory occupation of the measurement matrix is also large.…”