Low-Complexity Rate-Distortion Optimization of Sampling Rate and Bit-Depth for Compressed Sensing of Images (original) (raw)

Quantized Compressive Sensing Video Compression Framework for Low Power Applications

Compressive sensing is an approach to reduce the acquired signal dimension with a sampling rate lower than the Nyquist rate. This is achieved by incorporating suitable quantization techniques, such as scalar quantization, to compensate for the low sampling rate. However, quantization of small compressive sensing measurements does not perform well in terms of rate-distortion. This paper presents an adaptive variant of differential pulse code modulation coupled with scalar quantization for quantizing and de-quantizing the compressive sensing measurements of videos. The proposed adaptive approach along with scalar quantization allows reduction of the necessary bandwidth and provides a higher prediction gain than the conventional differential pulse code modulation. The performance of the proposed approach is validated by integrating with various compressive sensing reconstruction schemes and compared with the conventional video codec approach. The reconstructed video frames' visual ...

Recovery of quantized compressed sensing measurements

SPIE Proceedings, 2015

Compressed Sensing (CS) is a novel mathematical framework that has revolutionized modern signal and image acquisition architectures ranging from one-pixel cameras, to range imaging and medical ultrasound imaging. According to CS, a sparse signal, or a signal that can be sparsely represented in an appropriate collection of elementary examples, can be recovered from a small number of random linear measurements. However, real life systems may introduce non-linearities in the encoding in order to achieve a particular goal. Quantization of the acquired measurements is an example of such a non-linearity introduced in order to reduce storage and communications requirements. In this work, we consider the case of scalar quantization of CS measurements and propose a novel recovery mechanism that enforces the constraints associated with the quantization processes during recovery. The proposed recovery mechanism, termed Quantized Orthogonal Matching Pursuit (Q-OMP) is based on a modification of the OMP greedy sparsity seeking algorithm where the process of quantization is explicit considered during decoding. Simulation results on the recovery of images acquired by a CS approach reveal that the modified framework is able to achieve significantly higher reconstruction performance compared to its naive counterpart under a wide range of sampling rates and sensing parameters, at a minimum cost in computational complexity.

Performance analysis of algorithms for quantized compressed sensing

2018

Current data acquisition methods acquire massive amounts of data, which needs to be compressed, i.e. part of these data is discarded, in order to allow its storage or transmission. This is a wasteful and excessive work. The new emerging compressive sensing (CS) concept enables directly representing the signals with far fewer measurements than required by current techniques, and resolving the signals from these fewer measurements. This is made possible by exploiting the inherent redundancy of the signals, which is translated to sparsity in a transform domain. CS can recover the sparse signal accurately using various techniques: convex optimization algorithms (i.e. Basis Pursuit (BP)), greedy algorithms (i.e. Orthogonal Matching Pursuit (OMP)) and projected gradient descent algorithms (i.e. Iterative Hard Thresholding (IHT)). In classical CS the resulting measurements values are real values and need to be quantized. As the quantization part is the main burden and main source of error ...

Compressive Sensing based Image Compression and Recovery

Compressive sensing is a new paradigm in image acquisition and compression. The CS theory promises recovery of images even if the sampling rate is far below the nyquist rate. This enables better acquisition and easy compression of images, which is more advantageous when the resources at the sender side are scarce. This paper shows the CS based compression and two recovery two methods i.e., l1 optimization and TSW CS recovery. Experimental results show that CS provides better compression, and TSWCS provides better recovery with less relative error recovery than l1 optimization. It is also observed that use of increased measurements leads to reduced error.

Compressive Sensing Based Image Compression and Transmission for Noisy Channels

This paper presents the design of an optimized Compressive Sensing image compression technique for data transmission over noisy mobile wireless channel. The proposed technique is more robust to channel noise. It uses individual measurement driven coding scheme, which facilitates simpler encoder design. The shift of computational burden from encoder to decoder is more suitable for mobile devices applications where computational power and battery life are limited. This paper also presents a novel quantizer which allows the encoder to dynamically adapt to the channel conditions and provides optimum performance.

On the Rate-Distortion Performance of Compressed Sensing

2007

Encouraging recent results in compressed sensing or compressive sampling suggest that a set of inner products with random measurement vectors forms a good representation of a source vector that is known to be sparse in some xed basis. With quantization of these inner products, the encoding can be considered universal for sparse signals with known sparsity level. We analyze the operational ratedistortion performance of such source coding both with genie-aided knowledge of the sparsity pattern and maximum likelihood estimation of the sparsity pattern. We show that random measurements induce an additive logarithmic rate penalty, i.e., at high rates the performance with rate R + O(log R) and random measurements is equal to the performance with rate R and deterministic measurements matched to the source.

Effective Image Reconstruction Using Various Compressed Sensing Techniques

IEEE Conference , 2024

The prevailing information relies heavily on the principles articulated by Shannon and Nyquist. These theories assert that, to faithfully reconstruct a signal without distortion, the sampling frequency must exceed twice the signal's maximum frequency to prevent aliasing. Following this, signals undergo compression to eliminate inherent redundancies before transmission over the channel. Despite the effectiveness of this approach, a significant drawback arises from the substantial processing overhead involved in sampling and compression. This limitation renders the scheme unsuitable for contemporary applications, given the constraints of current computational capabilities. Compressive Sensing (CS) introduces a novel framework, grounded in signal decomposition and approximation theory. Serving as an alternative to the Nyquist criteria, CS presents advantages such as reduced sensing time and sampling rate. In this approach, signals are sampled below the Nyquist rate through linear projection onto a random basis, ensuring exact reconstruction of the original signal. CS contributes to the reduction of power consumption and computational complexity in handling digital data. The extraction of information is facilitated by the utilization of a sensing matrix. In the context of image restoration, the CS framework provides an innovative approach to recover highquality images from their compressed measurements. The success of image restoration in compressive sensing relies on the development of robust algorithms that can efficiently exploit sparsity while addressing the inherent trade-off between accuracy and computational complexity. We survey state-of-theart reconstruction algorithms, including iterative methods, convex optimization, and deep learning approaches, showcasing their strengths and limitations in restoring images from compressed measurements. The success of image restoration in compressive sensing relies on the development of robust algorithms that can efficiently exploit sparsity while addressing the inherent trade-off between accuracy and computational complexity. We survey state-of-the-art reconstruction algorithms, including iterative methods, convex optimization, and deep learning approaches, showcasing their strengths and limitations in restoring images from compressed measurements.

Image Compression using DCT based Compressive Sensing and Vector Quantization

International Journal of Computer Applications, 2012

Compressive sensing (CS) provides a mathematical framework for utilizing the potentiality of sparse nature of the commonly used signals and has been the subject of scientific research in recent years. CS involves the compression of the data at the first step of image acquisition. This paper presents an image compression algorithm based on DCT based CS and Vector Quantization (VQ). It has been observed from the implementation of the Proposed CS-VQ algorithm that the proposed algorithm gives better PSNR and visual quality when compared with the existing CS-VQ algorithm. The results obtained are even comparable with JPEG algorithm but only when small queue size is considered. The basic concept behind the CS states that small collections of non-adaptive linear projections of a sparse signal can efficiently helps in the reconstruction of the image through the image data sent to the decoder making use of some optimization procedure.

Quantization effects on Compressed Sensing Video

2010 17th International Conference on Telecommunications, 2010

Compressed Video Sensing (CVS) is the application of the theory and principles of Compressed Sensing to video coding. Previous research has largely ignored the effects of quantization on the random measurements. In this paper, we showed that Gaussian quantization of the CVS coefficients produce higher quality reconstructed videos compared to using MPEG and uniform quantization. Furthermore, the quantization matrix is robust against variations in the mean and standard deviations of the CS measurements among frames. Our work shows how quantization can be implemented for a practical CVS codec.