www.ijecs.in International Journal Of Engineering And Computer Science ISSN: 2319-7242 Volume 5 Issue 5 May 2016, Page No. 16704-16707 S.Spurthi, IJECS Volume 05 Issue 5 May 2016 Page No.16704-16707 Page 16704 Block Based Compressed Sensing Algorithm for Medical Image Compression S.Spurthi, Parnasree Chakraborty Department of electronics and communication B.S Abdur Rahman University Chennai, India spurthisingha@gmail.com Department of electronics and communication B.S Abdur Rahman University Chennai, India prernasree@bsauniv.ac.in Abstract— Block Compressive sensing technique has been proposed to exploit the sparse nature of medical images in a transform domain to reduce the storage space. Block based compressive sensing is applied to dicom image, where original dicom image is divided in terms of blocks and each block is processed separately. The main advantage of block compressive sensing is that each block is processed independently and combined with parallel processing to reduce the amount of time required for processing. Compressed sensing exploits the sparse nature of images to reduce the volume of the data required for storage purpose. Inspired by this, we propose a new algorithm for image compression that combines compressed sensing with different transforms. Different sparse basis like discrete cosine transform, discrete wavelet transform and contourlet are used to compress the original input image. Among these transforms, Dct transform has block artifacts problem [14]. Wavelet transform can overcome the block artifacts introduced in the reconstructed image. Contourlet transform effectively captures smooth contours[4] and hence Contourlet transform provides better reconstruction quality image. In order to reconstruct original image, different techniques such as basis pursuit, orthogonal matching pursuit etc. are used at the decoder. Keywords—PSNR, SSIM, DCT, DWT, CT Introduction Compressive sensing (CS) is a technique used to compress and reconstruct the original signal [1] having a sparse representation in some basis. CS can be applied effectively to the sparse signals. To get sparse representation basis such as DCT or DWT or CT .Equation (1) describes generation of the sparse signal s measurement matrix (A).dct basis is based on cosine functions and transformation kernel is generated .wavelet basis is based on filter bank structure contourlet transform basis is based on direction filter bank structure .after applying to basis function Then the sparse signal further compressed as y with a suitable measurement matrix (M). I. BASIS OF DIFFERENT TRANSFORMATION A. DISCRETE COSINE TRANSFORM: DCT transformation most popularly used transform and it is based on cosine functions[3] .DCT plays very important role for energy compaction property which is most important for image compression The 2D discrete cosine transform (2D DCT) can be expressed by Where p(x, y) is the element of the image represented by matrix p N is the size of image. i, j represents the transformed image from pixel matrix dct transform leads to block artifact problem .These artifacts involes as a regular pattern of visible block boundaries. S=psi*x (1) Where, x, is the input signal, psi is obtained by basis function. T is the Transform matrix or kernel and s is the sparse representation of the input data. After sparse generation, equation (1) expresses the generation of compressed sparse signal with the help of a randomly generated matrix A. The compressed sparse output y is given in Equation (2) y=A*S (2) The input signal x is converted into sparse signal s by applying suitable transform matrix DCT/CT/DWT - [T]. Then the sparse signal further compressed as y with a suitable B. DISCRETE WAVELET TRANSFORM Discrete Wavelet Transform (DWT) of a signal x (n) is obtained by by using Filter banks for wavelet transform. [5] First the data are passed through a low pass filter and has impulse response g (n) giving particular coefficients. Signal decomposition by using a high pass filter h (n), giving the more no of coefficients. The low pass filter gives approximate coefficients LL LH HL HH Fig 1. Wavelet Decomposition Using Four Sub Bands wavelet transform decomposes an image in to four sub bands