Compressive sensing with modified Total Variation minimization algorithm (original) (raw)

Review of Algorithms for Compressive Sensing of Images

We provide a comprehensive review of leading algorithms for compressive sensing of images, focused on Total variation methods, with a view to application in LiDAR systems. Our primary focus is providing a full review for beginners in the field, as well as simulating the kind of noise found in real LiDAR systems. To this end, we provide an overview of the theoretical background, a brief discussion of various considerations that come in to play in compressive sensing, and a standardized comparison of off-the-shelf methods, intended as a quick-start guide to choosing algorithms for compressive sensing applications.

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 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 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 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.

Image Denoising Using a Compressive Sensing Approach Based on Regularization Constraints

2022

In remote sensing applications, one of the key points is the acquisition, real-time pre-processing and storage of information. Due to the large amount of information present in the form of images or videos, compression of this data is necessary. Compressed sensing (CS) is an efficient technique to meet this challenge. It consists in acquiring a signal, assuming that it can have a sparse representation, using a minimal number of non-adaptive linear measurements. After this CS process, a reconstruction of the original signal must be performed at the receiver. Reconstruction techniques are often unable to preserve the texture of the image and tend to smooth out its details. To overcome this problem, we propose in this work, a CS reconstruction method that combines the total variation regularization and the non-local self-similarity constraint. The optimization of this method is performed by the augmented Lagrangian which avoids the difficult problem of non-linearity and non-differentia...

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).

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.

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...

A Novel Image Compressive Sensing Method Based on Complex Measurements

2011 International Conference on Digital Image Computing: Techniques and Applications, 2011

Compressive sensing (CS) has emerged as an efficient signal compression and recovery technique, that exploits the sparsity of a signal in a transform domain to perform sampling and stable recovery. The existing image compression methods have complex coding techniques involved and are also vulnerable to errors. In this paper, we propose a novel image compression and recovery scheme based on compressive sensing principles. This is an alternative paradigm to conventional image coding and is robust in nature. To obtain a sparse representation of the input, discrete wavelet transform is used and random complex Hadamard transform is used for obtaining CS measurements. At the decoder, sparse reconstruction is carried out using compressive sampling matching pursuit (CoSaMP) algorithm. We show that, the proposed CS method for image sampling and reconstruction is efficient in terms of complexity, quality and is comparable with some of the existing CS techniques. We also demonstrate that our method uses considerably less number of random measurements.