# Modelling and Analysis of Hybrid Transformation for Lossless Big Medical Image Compression
## 3 Proposed Methodology
### Proposed Algorithm
### Computational Performance of Wavelet Transform

The size of the filter set and the number of pixels in the image impact how quickly wavelet compression works. Although JPEG speed is related to the number of pixels, the DWT has substantially higher memory needs since the entire image must be changed simultaneously. In light of this, wavelet compression speed on a particular platform will be equivalent to JPEG compression speed for small pictures that can be stored entirely in memory but slower for bigger images. As an electronic file, the number of radiologic tests varies little between treatment techniques. A computed tomographic (CT) picture is 189 MB in size. A study with 40 images takes up roughly 16 MB for a two-view radiographic study and 20 MB for a study with 40 images. A typical MR picture is 8 MB; however, because many images are often collected, MR imaging examinations typically consume 10-15 MB. A cross-sectional picture may be decompressed using Windows NT 4.0 software (Microsoft, Redmond, Wash) in nanoseconds on a 200 MHz Pentium Pro computer with 64 MB of random access memory. A 10 MB radiograph may be decompressed using wavelet compression in around 9 s, compared to 7 s using the JPEG method. Standard modems may often operate via telephone lines at 28.8 kbit/sec rates. A 15 MB file would take roughly 90 min to transfer. A 10:1 compression ratio would cut the transmission time to 9 min, and a 33:1 ratio would lower it to 3 min. The improvement in transmission time is directly proportionate to the compression ratio employed. The compression ratio also linearly reduces the storage needed; for example, a 15:1 compression ratio would reduce the 15 MB research to just 1 MB [25; 26; 27; 28; 29; 30; 31; 32]. ```
1: Apply the improved embedding to the medical image. 2: Perform the extraction operation. 3: Apply the hard threshold using \[y_{hard}(t)=x(t)\ when\ abs(x(t))>T\] \[y_{hard}(t)=0,\quad\ when\ abs(x(t))\leq T\]
4: Perform the soft threshold using \[y_{soft}(t)=x(t)-T\ when\ abs(x(t))>T\] \[y_{soft}(t)=0,\quad\ when\ abs(x(t))\leq T\]
5: Find the entropy encoding h(s). \[h(s)=-\sum_{j=1}^{q}p(s_{i})log\ p(s_{i})\]
6: Determine the Shannon entropy M(C(b))). 7: Apply the wavelets based multi resolution analysis. 8: Define the Haar transform \(l_{k,\ n}=[k2^{-n},(k+1)2^{-n}]\)
9: Perform the dilation using \[\varnothing(x)=\sqrt{2}\sum_{k\in z}\varnothing(-k+2x)h(k)\]
10: Apply the wavelet operation using \[\varphi(x)=\sqrt{2}\sum_{k\in z}g(-k+2x)g(k)\]
11: Perform filtering operations using orthogonal quadrature. \[\psi_{a,b}(t)=2^{-a/2}\psi\big{(}2^{-a}t-b\big{)} \tag{2}\]0 \[\psi_{a,b}(t)=2^{-a/2}\psi\big{(}2^{-a}t-b\big{)} \tag{2}\]1
12: Apply the filters using bi-orthogonal quadrature. 13: Decompose the image using wavelets and apply the color conversion. ```
**Algorithm 3**Proposed Image Compression
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1: Apply the improved embedding to the medical image. 2: Perform the extraction operation. 3: Apply the hard threshold using \[\psi_{a,b}(t)=2^{-a/2}\psi\big{(}2^{-a}t-b\big{)} \tag{2}\]2 \[\psi_{a,b}(t)=2^{-a/2}\psi\big{(}2^{-a}t-b\big{)} \tag{2}\]3
4: Perform the soft threshold using \[\psi_{a,b}(t)=2^{-a/2}\psi\big{(}2^{-a}t-b\big{)} \tag{2}\]4 \[y_{soft}(t)=0,\quad\ when\ abs