Compressive Video Sampling With Approximate Message Passing Decoding

Abstract

In this paper, we apply compressed sensing to video compression. Compressed sensing (CS) techniques exploit the observation that one needs much fewer random measurements than given by the Shannon-Nyquist sampling theory to recover an object if this object is compressible (i.e., sparse in the spatial domain or in a transform domain). In the CS framework, we can achieve sensing, compression and denoising simultaneously. We propose a fast and simple online encoding by application of pseudo-random downsampling of the two-dimensional fast Fourier transform to video frames. For off-line decoding, we apply a modification of the recently proposed approximate message passing (AMP) algorithm. The AMP method has been derived using the statistical concept of 'state evolution', and it has been shown to considerably accelerate the convergence rate in special CS-decoding applications. We shall prove that the AMP method can be rewritten as a forward-backward splitting algorithm. This new representation enables us to give conditions that ensure convergence of the AMP method and to modify the algorithm in order to achieve higher robustness. The success of reconstruction methods for video decoding also essentially depends on the chosen transform, where sparsity of the video signals is assumed. We propose to incorporate the 3D dual-tree complex wavelet transform that possesses sufficiently good properties of directional selectivity and shift invariance while being computationally less expensive and less redundant than other directional 3D wavelet transforms.

Optimal-correlation-based reconstruction for distributed compressed video sensing

“…Zheng and Jacobs [11] presented a differencing method in order to take advantage of the spatial redundancy between neighboring frames, but it is only suitable for sequences that have small spatial changes. In [12], Ma et al proposed a modified approximate message passing algorithm to recover the undersampled videos, by using the 3D dual-tree complex wavelet transform with some correlation noise. Liu et al presented a motion-aware decoding method [13] for compressively sampled videos and a maximum frame rate video acquisition framework was proposed in [14].…”

Object detection oriented video reconstruction using compressed sensing

“…CS can perform image sensing and compression simultaneously with low computational complexity. It has the superiority in reducing the computational cost of video encoder [11]. Due to its advantages, CS has become an attractive solution in object detection.…”

Reconstruction of compressed-sensed video using compound regularization

“…One kind of methods performs joint reconstruction of sub-video sequences. e.g., Ma et al [4] apply a modification of the approximate message passing algorithm and propose incorporating 3-D dualtree complex wavelet transform during reconstruction. Li et al [5] recover video cubes by minimizing TV norm of the pixelwise discrete cosine transform (DCT) coefficients along the temporal direction.…”