A Novel Image Compressive Sensing Method Based on Complex Measurements (original) (raw)

Compressive Sensing Based Image Reconstruction using Wavelet Transform

International Journal of Engineering and Technology

Compressive Sensing is a novel technique where reconstruction of an image can be done with less number of samples than conventional Nyquist theorem suggests. The signal will pass through sensing matrix wavelet transformation to make the signal sparser enough which is a criterion for compressive sensing. The low frequency and high frequency components of an image have different kind of information. So, these have to be processed separately in both measurements and reconstruction techniques for better image compression. The performance further can be improved by using DARC prediction method. The reconstructed image should be better in both PSNR and visual quality. In medical field, especially in MRI scanning, compressive sensing can be utilized for less scanning time. Keyword-Compressive Sensing, Wavelet transform, Sparsity, DARC prediction I. INTRODUCTION Compressive sensing (CS) is a new compression technique where fewer samples of measurement are enough to reconstruct the image with good visual quality. The samples required are much lesser than Nyquist criterion suggests. But the non-linear reconstruction used in CS is more complex compared to linear reconstruction in conventional compression. CS will measure finite dimensional vectors. Now CS is actively researched in applications like MRI, RADAR, single pixel camera, etc. as in [1]. We consider the application in medical field. MR images are sparse in Wavelet domain. The medical images will undergo CS so that the image reconstructed will have good visual quality but with less number of measurements. MRI is slow process due to the large number of data needed to be collected while scanning a patient as in [2]. With the help of CS we can reduce the number of samples, thus reducing scan time, which will benefit patient with less radiation exposure. In CS, there are three main principles-Sparsity, Measurements taking and Nonlinear reconstruction. The signal should be sparse-Information rate contained in the image should be much less than bandwidth-to undergo CS. If it's not sparse enough; we need to undergo the transformation of the image to make it sparse. We took wavelet transform as sparsity inducing matrix in this paper. The reconstruction of signals from lesser samples can only be possible if the chosen sparsity matrix and measurement matrix follows Restricted Isometry Property. The incoherence between these matrices is necessary for this. There are two approaches for reconstructing image at receiver side-basis pursuit and greedy algorithm. These nonlinear techniques will result in good quality reconstructed image as in [3]. In short, CS helps to reduce sampling and computation costs for sensing signals that have a sparse or compressible representation. In paper [4], the authors introduced a novel compressive sensing based prediction measurement (CSPM) encoder. The sparse image undergoes CS by using Gaussian matrix and these measured values pass to CSPM. In CSPM, the measured matrix undergoes linear prediction and entropy encoding. Since the sparsity level of prediction residual is higher than its original image block, the performance of CS image reconstruction algorithm will be better. This CSPM encoder can achieve significant reduction in data storage and saves transmission energy. The bandwidth consumption of CSPM based CS will be considerably less which in turn increases the lifetime of sensors. The wavelet transformed image has high frequency coefficients that are sparse and the low frequency coefficients that are not sparse. The low-frequency coefficients contain most of the energy of the image and have coherent nature. In paper [5], they measured (CS applied) the high-frequency sub band coefficients, and kept the low-frequency sub-band coefficients unchanged. In this paper we have chosen deterministic matrices such as Hadamard matrix, random matrices such as Gaussian matrix, as measurement matrices and to attain sparsity the Daubechies wavelets are used. The nonlinear reconstruction methods used are Orthogonal Matching Pursuit (OMP) and L1 minimisation technique. The prediction methods used are Linear and DARC.

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 Reconstruction

2017

Compressive Sensing is novel technique where reconstruction of an image can be done with less number of samples than conventional Nyquist theorem suggests. The signal will pass through sensing matrix wavelet transformation to make the signal sparser enough which is a criterion for compressive sensing. Different levels of wavelet decomposition are also analyzed in this paper. The performance further can be improved by using DARC prediction method. The prediction error signal transmitted through OFDM channel. The reconstructed image should be better in both PSNR and bandwidth. Medical field especially in MRI scanning, compressive sensing can be utilized for less scanning time.

A Study on Compressive Sensing and Reconstruction Approach

Journal of emerging technologies and innovative research, 2015

This paper gives the conventional approach of reconstructing signals or images from calculated data by following the well-known Shannon sampling theorem. This principle underlies the majority devices of current technology, such as analogto-digital conversion, medical imaging, or audio and video electronics. The primary objective of this paper is to establish the need of compressive sensing in the field of signal processing and image processing. Compressive sensing (CS) is a novel kind of sampling theory, which predicts that sparse signals and images can be reconstructed from what was in the past thought to be partial information. CS has two distinct major approaches to sparse recovery that each present different benefits and shortcomings. The first, l1-minimization methods such as Basis Pursuit use a linear optimization problem to recover the signal. This method provides strong guarantees and stability, but relies on Linear Programming, whose methods do not yet have strong polynomia...

Sparse signal, image recovery in compressive sensing technique through l1 norm minimization

2012

The classical Shannon Nyquist theorem tells us that, the number of samples required for a signal to reconstruct must be at least twice the bandwidth of the highest frequency for the signal of interest. In fact, this principle is used in all signal processing applications. Unfortunately, in most of the practical cases we end up with far too many samples. In such cases a new sampling method has been developed called Compressive Sensing (CS) or Compressive Sampling, where one can reconstruct certain signals and images from far fewer samples or measurements when compared to that of samples in classical theorem. CS theory primarily relies on sparsity principle and it exploits the fact that many natural signals or images are sparse in the sense that they have concise representations when expressed in the proper basis. Since CS theory relies on sparsity, we focused on reconstructing a sparse signal or sparse approximated image from its corresponding few measurements. In this document we focused on 1 l norm minimization problem (convex optimization problem) and its importance in recovering a sparse signal or sparse approximated image in CS. To sparse approximate the image we have transformed the image form standard pixel domain to wavelet domain, because of its concise representation. The algorithms we used to solve the 1 l norm minimization problem are primal-dual interior point method and barrier method. We came up with certain examples in Matlab to explain the differences between barrier method and primal-dual interior point method in solving a 1 l norm minimization problem i.e. recovering a sparse signal or image from very few measurements. While recovering the images the approach we used is block wise approach and treating each block as vector.

Compressive Sensing Algorithms for Signal Processing Applications: A Survey

International Journal of Communications, Network and System Sciences, 2015

In digital signal processing (DSP), Nyquist-rate sampling completely describes a signal by exploiting its bandlimitedness. Compressed Sensing (CS), also known as compressive sampling, is a DSP technique efficiently acquiring and reconstructing a signal completely from reduced number of measurements, by exploiting its compressibility. The measurements are not point samples but more general linear functions of the signal. CS can capture and represent sparse signals at a rate significantly lower than ordinarily used in the Shannon's sampling theorem. It is interesting to notice that most signals in reality are sparse; especially when they are represented in some domain (such as the wavelet domain) where many coefficients are close to or equal to zero. A signal is called K-sparse, if it can be exactly represented by a basis, { } 1 ψ N i i = , and a set of coefficients k x , where only K coefficients are nonzero. A signal is called approximately K-sparse, if it can be represented up to a certain accuracy using K non-zero coefficients. As an example, a K-sparse signal is the class of signals that are the sum of K sinusoids chosen from the N harmonics of the observed time interval. Taking the DFT of any such signal would render only K non-zero values k x. An example of approximately sparse signals is when the coefficients k x , sorted by magnitude, decrease following a power law. In this case the sparse approximation constructed by choosing the K largest coefficients is guaranteed to have an approximation error that decreases with the same power law as the coefficients. The main limitation of CS-based systems is that they are employing iterative algorithms to recover the signal. The sealgorithms are slow and the hardware solution has become crucial for higher performance and speed. This technique enables fewer data samples than traditionally required when capturing a signal with relatively high bandwidth, but a low information rate. As a main feature of CS, efficient algorithms such as 1 -minimization can be used for recovery. This paper gives a survey of both theoretical and numerical aspects of compressive sensing technique and its applications. The theory of CS has many potential applications in signal processing, wireless communication, cognitive radio and medical imaging.

A new wavelet based efficient image compression algorithm using compressive sensing

Multimedia Tools and Applications, 2015

We propose a new algorithm for image compression based on compressive sensing (CS). The algorithm starts with a traditional multilevel 2-D Wavelet decomposition, which provides a compact representation of image pixels. We then introduce a new approach for rearranging the wavelet coefficients into a structured manner to formulate sparse vectors.

Various Applications of Compressive Sensing in Digital Image Processing: A Survey

Compressive sensing (CS) is a fast growing area of research. It neglects the extravagant acquisition process by measuring lesser values to reconstruct the image or signal. Compressive sensing is adopted successfully in various fields of image processing and proved its efficiency. Some of the image processing applications like face recognition, video encoding, Image encryption and reconstruction are presented here.

On the Use of Compressive Sensing for Image Enhancement

Compressed Sensing (CS), as a new rapidly growing research field, promises to effectively recover a sparse signal at the rate of below Nyquist rate. This revolutionary technology strongly relies on the sparsity of the signal and incoherency between sensing basis and representation basis. Exact recovery of a sparse signal will be occurred in a situation that the signal of interest sensed randomly and the measurements are also taken based on sparsity level and log factor of the signal dimension. In this paper, compressed sensing method is proposed to reduce the noise and reconstruct the image signal. Noise reduction and image reconstruction are formulated in the theoretical framework of compressed sensing using Basis Pursuit (BP) and Compressive Sampling Matching Pursuit (CoSaMP) algorithm when random measurement matrix is utilized to acquire the data. In this research we have evaluated the performance of our proposed image enhancement methods using the quality measure peak signal-to-noise ratio (PSNR).

Sparse Signal Representation, Sampling, and Recovery in Compressive Sensing Frameworks

IEEE Access

Compressive sensing allows the reconstruction of original signals from a much smaller number of samples as compared to the Nyquist sampling rate. The effectiveness of compressive sensing motivated the researchers for its deployment in a variety of application areas. The use of an efficient sampling matrix for high-performance recovery algorithms improves the performance of the compressive sensing framework significantly. This paper presents the underlying concepts of compressive sensing as well as previous work done in targeted domains in accordance with the various application areas. To develop prospects within the available functional blocks of compressive sensing frameworks, a diverse range of application areas are investigated. The three fundamental elements of a compressive sensing framework (signal sparsity, subsampling, and reconstruction) are thoroughly reviewed in this work by becoming acquainted with the key research gaps previously identified by the research community. Similarly, the basic mathematical formulation is used to outline some primary performance evaluation metrics for 1D and 2D compressive sensing. INDEX TERMS Compressed sensing, compressive sampling, reconstruction algorithms, sensing matrix. IRFAN AHMED received the B.Sc. and M.Sc. degrees in electrical engineering and the Ph.D. degree in computer systems engineering from the University of Engineering & Technology Peshawar. He is currently employed as a full-time Lecturer with the