Problem:- In Pixel Fusion of CT scan main problem
is due to multiple re-projection and back-projection operation during image
iterative reconstruction. The sinogram restoration algorithms often suffer from
noticeable resolution loss especially in the case of constant noise variance. Pixel-level
image fusion is to combine visual information contained in multiple source
images into an informative fused image without the introduction of distortion
or loss of information with Alignments of different wavelengths and frequency
with different hardware to perform many different algorithms for perfect fusion
in RGB.

__Background__

The main emphasis of the latest
developments in medical imaging is to develop more reliable and capable algorithms
which can be used in real time diagnosis of tumours’. Brain tumour is caused
due to uncontrolled growth of a mass of tissue, which can be fatal among
children and adults. Depending on the
origin and growth, brain tumor can be classified into two types: 1) primary
brain tumor is developed at the original site of the tumor 2) secondary brain
tumor is the cancer which spreads to the other parts of the body. The detection
of brain tissue and tumor in MR images and CT scan images has been an active research
area. Segmenting and detection of
specific regions of brain containing the tumor cells is considered to be the
fundamental problem in image analysis related to tumor detection. Many
segmentation algorithms are implemented based on edge detection on the grey
scale images

The contrast pyramid fusion method
loses too much source information to obtain a clear, subjective image; the
ratio pyramid method produces lots of inaccurate information in the fused
version, and the morphological pyramid method creates a large number of
artifacts that do not exist in the original source images. Wavelets and their
related transform represent another widely used technique in this category. Wavelet
transforms provide a framework in which an image is decomposed into a series of
coarse-resolution sub-bands and multi-level finer-resolution sub-bands. {3}

Statistical iterative
reconstruction (SIR) {2}, methods, by modelling the noise properties of the
measurements and imposing adequate regularization within image reconstruction,
can achieve a performance superior to other existing methods in terms of noise
reduction and noise-resolution tradeoff. A critical problem in SIR is the high
computational burden due to the multiple re-projection and back-projection
operations during image iterative reconstruction. To overcome this, restoring
the ideal sinogram data from acquired noisy one and reconstructing the CT image
from the estimated ideal sonogram data is an interesting alternative strategy
with computational efficiency and noise-induced artifact suppression.

CT scan is lower the
mill-ampere-second (mAs)as low as reasonably achievable in data acquisition
with lower-mAs scans (or low-dose scans) will be unavoidably degraded due to
the excessive data noise, if no adequate noise control is applied during image
reconstruction. For image reconstruction with low-dose scans, sonogram
restoration algorithms based on modelling the noise properties of measurement
can produce an image with noise-induced artefact suppression, but they often suffer
noticeable resolution loss.{7}

__Motivation__

Progress on medical image fusion
techniques has been made, and various fusion algorithms have been developed.
Medical image fusion can be performed at three broad levels: pixel level,
feature level, and decision level. Pixel based {2} fusion is performed on a
pixel-by-pixel basis, generating a fused image in which information associated
with each pixel is selected from a set of pixels in the source images. Medical
image fusion at the feature level requires the extraction of salient
environment-dependent features, such as pixel intensities, edges, or textures.
Decision-level fusion involves merging information at a higher level of abstraction, combining the results from
multiple algorithms to yield a final fused decision {5}. At this level, input
images are processed individually for information extraction. The obtained
information is then combined by applying decision rules to reinforce a common
interpretation.

At the pixel-level of medical
image fusion, the simplest method is to average the input images to generate a
fused version. This method will heavily degrade the brightness of the input
images. The IHS fusion converts a low-resolution color image from the RGB space
into the IHS color space.

Wang,et al. {10}proposed the
KL-PWLS algorithm to de-correlate data signals along nearby projection views
for CT sonogram restoration by employing the KL transform. The adapted KL
transform with dimension 3*3 was first applied to account for the correlative
information of continuous data sampling along nearby of the sonogram data. Let
ÿ1 and y denote the KL transformed components and the corresponding original
originals sonogram data in the spatial domain. Then, in the KL domain, the PWLS
criterion can be used to estimate the ith KL component ᶈ of ideal sonogram data
from the ith KL component ÿ1 of original sonogram data by minimizing the
following objective function.

{10}
where

˙l is the diagonal variance matrix and can be estimated from
the variance

of

the original sinogram data

at detector bin i and view k. The scalar β is
a hyper- parameter, di is the the eigen value of the lth KL basic vector, and

is the penalty term. The original sonogram
data y has a unique property which can expressed by a relationship between the
sample mean and variance:

{10}

__Research Methodology__

__The ndiNLM Algorithm:-__

A normal-dose Ct image scanned
previously may be available in some clinical applications such as CT perfusion
Imaging and CT angiography, the previous normal-dose scan can provide a
reference image to construct more reasonable non-local weights than those used
in original NLM algorithm{17} for low-dose CT image restoration. With this
observation, the ndiNLM algorithm was proposed:-

{17}
{17}
The proposed sinogram restoration
induced non-local means (SR-NLM) algorithm adapts the ndiNLM algorithm to
exploit more reasonable similarity information in the FBP image reconstructed
from the KL-PWLS restored low-dose sinogram data, instead of the FBP image{17}
reconstructed from the original low-dose sinogram data. Specifically, the
SR-NLM algorithm contains four major steps:

(a) direct FBP image reconstruction

direct from the original low-dose sinogram
data; just putting data for process for 3 step.

(b) sinogram restoration using the
KL-PWLS algorithm and FBP image reconstruction

from the KL-PWLS restored sinogram data; sonogram
restoration by FBP and pwls values for 3 step

{17}

(d) non-local weighted average
using the calculated non-local means weights, after the non local weight
construction, according to SR-NLM Image Fusion algorithm can be executed via
non-local weighted average operation-

Fig:-Three digital phantoms used for computer simulation
studies. (a) The modified clock phantom contains eight inserts with varying
contrast (C1: +30%, C2: −7%, C3: −15%,
C4: +85%, C5: −30%, C6: +7%, C7: +15%, and C8:−85%). Eight ROIs marked by larger squares allow comparison
of zoomed images. ROI 1, ROI 2 and background region indicated by small squares
allow comparison of the contrast-to-noise ratio. The lines along the edges of
the inserts (C1 and C4) allow comparison of the noise-resolution tradeoff; (b)
the image of one slice of XCAT phantom with a lesion (contrast of +15%) as
indicated by a square. Two ROIs marked by two squares allow visual inspection comparison
of zoomed images; and (c) the modified Shepp–Logan phantom with a low-contrast
small lesion (contrast of +1.5%) as indicated by the arrow.

__Research Issues in Multi-Slice CT
scan Image fusion:-__

__Pixel Solution
of ndiNLM Algorithm.__
__Signal Reduction
for wavelength.__
__Exogenous
source priors.__

__Fusion Solution
for Pixel under ndiNLM Algorithm __

Markov random fields (MRFs) are
used to perform fusion {12} regularization by imposing prior knowledge on the
types of admissible images fusion, depth maps, flow fields, and so on. While
such models have proven useful for regularizing problems in computer image
fusion, MRFs have mostly been limited in three respects:

(1) They have used very simple neighborhood
structures. Most models in low-level vision are based on pairwise graphs, where
the potential functions are formulated in terms of pixel fusion differences
(image derivatives) between neighboring sites. Fusion are dissected into an
assembly of nodes that may correspond to pixels or agglomerations of pixels
fusion. Hidden variables associated with
the nodes are introduced into a model designed to “explain” the values (colors)
of all the pixels fusion.

(2) In many cases, potentials
have remained hand-defined and hand-tuned. Consequently, many MRFs do not
necessarily reflect the statistical properties of the image fusion. The direct
statistical dependencies between hidden variables are expressed by explicitly grouping
hidden variables;

(3) MRF models have typically not been
spatially adaptive, that is, their potentials do not depend on the spatial
location within the image fusion with pixel.

Analysis of the marginal
statistics of steered derivative filter responses (figure) reveals that while
both are heavy-tailed, the derivative orthogonal to the image structure has a
much broader histogram than the aligned derivative. The SRF potentials model
these steered filter responses using a Gaussian scale mixture (GSM) , which is more
flexible than many previous potential functions and is able to capture their
heavy-tailed characteristics.

**Fig. 2. **The clock phantom images reconstructed by different methods and eight
zoomed regions indicated by the marks
with C1 to C8 in Fig. 1(a). (a) The conventional FBP image fusion with ramp
filter reconstructed from the original sinogram data; (b) the standard FBP
image reconstructed from the restored sinogram data by the KL-PWLS algorithm
with ˇ = 400; (c) the conventional FBP image restored
by the original NLM algorithm with _ = 5.6 ×10−3; and (d) the reconstructed FBP image restored by the
present SR-NLM algorithm with ˇ = 400, _ = 1.4×0−3. All images are displayed with
same window.

__Signal Reduction
for wavelength:-__

In order to evaluate the
performance of the present SR-NLM in a more quantitative manner for image
fusion, the peak signal-to-noise ratio (PSNR) and normalized mean square error
(NMSE) merits were used in this study. They are defined as:

{12}
{13}
where µ(k) represents the
intensity value at the pixel k in the image µ, µphantom(k) represents the
intensity value at the pixel k in the ideal phantom image, and K denotes the
number of image pixels fusion. max(µphantom) represents the maximum intensity
value of the ideal phantom image {17}.

**Fig. 3. **The horizontal profiles through the
center of bone insert (C4) and the dark insert (C5) in the reconstructed clock
phantom images fusion corresponding to Fig. 1 & 2 with Markov pixel fusion over wavelegth problem solution.

__Exogenous
source priors for Markov Model to Implement Fusion__ (for complex image fusion)

If there is prior knowledge that
activity is restricted to a volume of interest, the dipoles outside this volume
can be masked and the solution will be forced to be inside the specified
volume. However this procedure can lead to errors as all data, regardless of origin,
will be explained by activity in this volume. An alternative and preferred
approach is to use a soft constraint by creating extra components in the set C
that specify sources inside the volume of interest. The relationship between an
object model (no matter how accurate) and the object's image is a complex one.
The appearance of a small patch of a surface is a function of the surface
properties, the patch's orientation, the position of the lights and the
position of the observer.

Given a model u(x) and an image
v(y) we can formulate an imaging equation,

u(T(x))`= F(u(v),q)``

The advantage of this
configuration (CT scan with ndiNLM algorithm with Exogenous) is that by
separating the two systems axially, possible interference can be minimized, the
PET scanner design is not subject to geometric constraints imposed by the bore
size of the MR system, and existing PET and MRI systems might be able to be
used with relatively little modification. The process of constructing an
observation has two separate components. The first component is called a
transformation, or poses (T). It relates the coordinate frame of the model, x,
to the coordinate frame of the image. The imaging function determines the value
of image point u(T(x)). The second component is the imaging function, F(u(x),
q).The transformation tells us which part of the model is responsible for a
particular pixel of the image. In general a pixel's value may be a function
both of the model and other exogenous factors.

For
example, when functional CT scan data are available, regional activations can
be included as extra components in C, translating the CT scan information into
candidate MSP patches within the library (see Henson et al., 2010). These must be
soft constraints as one cannot assume that volume showing CT scan responses
will necessarily contribute to MEG/EEG data. Note that incorporating prior
knowledge in this way does not bias the estimate of source activity — rather it
allows the estimate to take non-zero values.

`u(T(x))= µ(phantom), ``F(u(x),q)=NMSE
{13} this is new derived algorithm with Morkov model for Pixel solution under
this Exogenous I had done the transformation of 3*3 image for the fusion with Eigen
values of normalized mean square error (NMSE) with Max wave length µ(phantom) and `u(T(x)) if
the transform value’s from output function values of phantom wavelength u(x),q.