Multi-scale/Multi-resolution Kronecker compressive imaging (original) (raw)

Spatially scalable Kronecker Compressive Sensing of Still Images

ompressivesensing(CS)hastofacewithtwochallengesofcomputationalcomplexityreconstructionandlow coding efficiency.As a solution,this paper presents a novelspatially scalable Kronecker two layer compressive sensing framework which facilitates reconstruction up to three spatialresolutions as wellas much improved CS coding performance.Weproposeadual-resolutionsensingmatrixbasedonthequincunxsamplinggridwhichisappliedtothe baselayer.Thissensingmatrixcanprovideafast-preview oflow resolutionimageatencodersidewhichisutilizedfor predictivecoding.Theenhancementlayerisencodedastheresidualmeasurementbetweentheacquiredmeasurementand predicted measurementdata.The low resolution reconstruction is obtained from the base layeronly while the high resolutionimageisjointlyreconstructedusing bothtwolayers.Experimentalresultsvalidatethattheproposedscheme outperformsbothconventionalsinglelayerandpreviousmulti-resolutionschemesespeciallyathighbitratelike2.0bppby 5.75dBand5.05dBPSNRgainonaverage,respectively.

Texture Preserving Recovery and Multi- Resolution Sensing Matrix for Kronecker Compressive Imaging

Compressive sensing (CS) has recently attracted considerable attention for its capability of simultaneous sampling and compression. CS produce high reconstruction performance based on the sparsity of signal in selected transform domain. However, CS still has challenges in low performance and computational complexity of reconstruction. Motivated by nonlocal structure of natural image and based on the cartoon texture image decomposition technique, this thesis proposes an efficient edges/textures preserving total variation based reconstruction algorithm. A fast implementation of the proposed method is presented using split Bregman method. Toward more efficient sensing scheme, we study hybrid sensing matrix with combination of deterministic DCT and Gaussian random matrices which efficient sample the similarity and difference of image but broke democracy property of CS. In order to overcome this drawback and provide fast reconstruction, we further develop a novel multi-resolution KCS sensing matrix which not only provides multi-resolution measurement, reduces reconstruction running time but also improves the final reconstruction performance. The proposed scheme are evaluated via convincing numerical experiments which shows significant improvement over the conventional scheme and competitive performance with other state of the art algorithms in terms of objective and subjective quality

Multi-resolution Kronecker Compressive Sensing

IEIE Trans. on Smart Processing and Computing, 2014

Compressive sensing is an emerging sampling technique which enables sampling a signal at a much lower rate than the Nyquist rate. In this paper, we propose a novel framework based on Kronecker compressive sensing that provides multi-resolution image reconstruction capability. By exploiting the relationship of the sensing matrices between low and high resolution images, the proposed method can reconstruct both high and low resolution images from a single measurement vector. Furthermore, post-processing using BM3D improves its recovery performance. The experimental results showed that the proposed scheme provides significant gains over the conventional framework with respect to the objective and subjective qualities.

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.

Practical compressive sensing of large images

2009 16th International Conference on Digital Signal Processing, 2009

Compressive imaging (CI) is a natural branch of compressed sensing (CS). One of the main difficulties in implementing CI is that, unlike many other CS applications, it involves huge amount of data. This data load has extensive implications for the complexity of the optical design, for the complexity of calibration, for data storage requirements. As a result, practical CI implementations are mostly limited to relative small image sizes. Recently we have shown that it is possible to overcome these problems by using a separable imaging operator. We have demonstrated that separable imaging operator permits CI of megapixel size images and we derived a theoretical bound for oversampling factor requirements. Here we further elaborate the tradeoff of using separable imaging operator, present and discuss additional experimental results.

Hybrid Kronecker Compressive Sensing for Images

IEEE ATC 2014, 2014

Natural images has certain level of both similarity and difference which can be efficiently represented by deterministic and random sensing matrices in compressive sensing. In this context, a hybrid sensing matrix which combines a deterministic DCT and a random matrix, is recently investigated. In this paper, we bring the concept of hybrid sensing matrix into Kronecker compressive sensing (KCS) of images. Extensive experiment has shown that the proposed hybrid KCS method performs better than either fully random or deterministic DCT matrix, and comparatively with other state-of the-art sensing schemes in terms of reconstruction quality.

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.

Compressive Image Sensing: Turbo Fast Recovery with Lower-Frequency Measurement Sampling

iis.sinica.edu.tw

In order to get better reconstruction quality from compressive sensing of images, exploitation of the dependency or correlation patterns among the transform coefficients has been popularly employed. Nevertheless, both recovery quality and recovery speed are not compromised well. In this paper, we study a new image sensing technique, called turbo fast compression image sensing, with computational complexity O(m 2 ), where m denotes the length of a measurement vector y = φx that is sampled from the signal x of length n via the sampling matrix φ with dimensionality m×n. In order to leverage between reconstruction quality and recovery speed, a new and novel sampling matrix is designed. Our method has the following characteristics: (i) recovery speed is extremely fast due to a closed-form solution is derived; (ii) certain reconstruction accuracy is preserved because significant components of x can be reconstructed with higher priority via an elaborately designed φ. Our method is particularly different from those presented in the literature in that we focus on the design of a sampling matrix without relying on exploiting certain sparsity patterns. Simulations and comparisons with state-of-the-art CS methodologies are provided and demonstrate the feasibility of the proposed method in terms of reconstruction quality and computational complexity.

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.