Post on 02-Jun-2018
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SUBMITTED TO:MR. SUMIT BUDHIRAJA
ASSTT. PROFESSOR
SUBMIITED BY : MEENAKSHIME-ECE (2ndYEAR)
ROLL NO. -13-713
UIET (P.U), CHD.
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Imaging
is a broad field which covers all aspects of theanalysis, modification, compression, visualization, andgeneration of images.
Image reconstruction can be seen as the solution of amathematical inverse problem in which the cause isinferred from the effect. As a consequence,measurement and recording techniques designed to
produce the images depend deeply on the applicationconsidered.
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Compressive sensing is a new type of sampling theory,
which predicts that sparse signals and images can be
reconstructed easily .
CS relies on the empirical observation that many types
of signals or image can be well-approximated by a
sparse expansion in terms of a suitable basis, that is, by
only a small number of non-zero coefficients to be
incomplete information.
A compression is obtained by simply storing only the
largest basic coefficients. When reconstructing the
signal the non-stored coefficients are simply set to zero
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The problem defined here is image reconstruction usingcompressive sensing technique. For that purpose, differenttechniques and parameter can be implemented and used.
The image at the decoder side can be recovered easily with somesparse information , thereby saving the storage memory, fewermeasurements and short scan time, reduce data rate and lowcomplexity encoders.
Sparsity expresses the idea that the information rate of acontinuous time signal may be much smaller than suggested by its
bandwidth and CS exploits the fact that many natural signals aresparse or compressible in the sense that they have conciserepresentations when expressed in the proper basis.
Incoherenceextends the duality between time and frequency andexpresses the idea that objects having a sparse representation inone domain mustbespread out in the domain in which they areacquired
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COMPRESSIVE SENSING
Compressed sensing relies on L1 techniques, which several other
scientific fields have used historically. In statistics, the least
squares method was complemented by the norm, which was
introduced by Laplace. It was used in matching pursuit in 1993
and basis pursuit in 1998. There were theoretical results describing when these algorithms
recovered sparse solutions, but the required type and number of
measurements were sub-optimal and subsequently greatly
improved by compressed sensing. At first glance, compressed
sensing might seem to violate the sampling theorem, becausecompressed sensing depends on the sparsity of the signal in
question and not its highest frequency but this is a misconception .
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Different intraprediction modes or intraprediction
modes can be considered concerning the smoothing
and boundary strength and various smoothing filters
like butterworth ,adaptive and kalman filters can be
used.
The effect of noise is not considered with every
minimizing technique, which is a crucial obstruction in
recovery.
While collecting the coefficients (sampling) can bebased on other side information too like contrast,
number of rows, permutations of the coefficients,
strength of pixel can be used. Earlier work has used
only variance and energy.
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The constraint of TV minimization can be
wavelet constraint, DCT constraint, radon
transform and norms can be considered along
with TV.Earlier work has rarely used domains like
contourlet, curvelet ,DDWT.
For OMP, various side information, variable
index set at each iterations, adaptive filtering
with the technique, sampling of residual
coefficients can be employed.
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Implementation of block compressive sensing and applying
transform like wavelet transform (Haar, Shear, Daubechies,),
DDWT (Dual tree Discreet Wavelet Transform), radon transform,
fourier transform in domains like spatial, contourlet, curvelet etc.
Design of Measurement matrix [15].TV minimization either byintraprediction modes , gradient descent method, norm method or
with side information and other constraints like DCT, Contourlet
[16].
Sampling optimization like adaptive (based on energy, variance ,
permutations of coefficients, kroneckor product). OMP with side information, applied only on high level
coefficients, with generalised form followed by smoothing filters.
Analysis of parameters like PSNR, Quantization noise with
respect to number of measurements, number of blocks.
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