Logarithmic Discrete Wavelet Transform for High-Quality Medical Image Compression

Logarithmic Discrete Wavelet Transform for High
Quality Medical Image Compression
By: Mohammed IBRAHEEM
29-03-2017
Prof. YANG-SONG Fan Reviewer
Prof. RABAH Hassan Reviewer
Prof. BENSRHAIR Abdelaziz Examiner
Prof. LEMIRE Daniel Examiner
Dr. HACHICHA Khalil Supervisor
M. HOCHBERG Sylvain Supervisor
Prof. GARDA Patrick Supervisor
Jury Members
Prof. MEHREZ Habib President

Outlines
29-03-201729-03-2017 LNS-DWT Mohammed IBRAHEEM – LIP6-UMPC-CIRA 33
IntroductionPart I
State of the artPart II
Logarithmic Library for image processingPart III
Logarithmic DWT based CompressionPart IV
2D-DWT Hardware ArchitecturePart V
Conclusion and Future workPart VI

Part I
IntroductionIntroduction
29-03-2017 LNS-DWT Mohammed IBRAHEEM – LIP6-UMPC-CIRA 4

ContextContext
E-health systems
Medical imaging technology growth
Resolution/Image size
E-health systems
Medical imaging technology growth
Resolution/Image size
Needs ?
 Archive
 Remote access
 Embedded solutions
Limitations ?
 Storage cost → huge numbers daily
o Full MRI exam can produce 10 GB
 Bandwidth
 limited resources on embedded systems

ChallengesChallenges
Trade-off between image quality/compression
 Vital information → preserving quality → avoid misdiagnoses
Q: How to achieve an efficient image compression while preserving the diagnostic quality?
First Challenge
Second Challenge Speed
Q: How to achieve a high-speed compression on Embedded systems?
The compression algorithm on embedded systems/limited resources
Time is a life saver

Part II
State of the artState of the art

Original
Image
Compressed
Image
Original
Image
Compressed
Image
Original
Image
Compressed
Image
Image Compression Algorithms Used in Medical domainImage Compression Algorithms Used in Medical domain
JPEG
Quant.DCT
Entropy
Encoder
Color
Space
Transform
Quant.DWT
Entropy
Encoder
Color
Space
Transform
Quant.DWT
HENUC
Encoder
Color
Space
Transform
 Based on DCT → Block artifacts
JPEG2000
 Two compression modes: lossy / lossless
 Based on DWT
 No block artifacts
WAAVES
 Two compression modes: lossy / lossless
 Based on DWT → No block artifacts
 Medical certified → clinical tests
 Efficient encoder
 Hierarchical Enumerative Coding

Image Quality Issues in Image CompressionImage Quality Issues in Image Compression
Quality
issues
Arithmetic
(Real numbers)
DWT/DCT
Quantization
(Division +
rounding)
Arithmetic alternatives in state of the art
• Floating-point
• Fixed-point
o Limited accuracy
o High speed - HW
 Simple div/mul operations
 Accuracy near to FLP
 An alternative to FLP on embedded systems
 Accelerate the DSP apps
Compressed
ImageQuant.
DWT
DCT
Encoder
Color
Space
Transform
Original
Image
Multiplication 𝒍𝒐𝒈 𝟐 𝒙 × 𝒚 = 𝒂 + 𝒃
Division 𝒍𝒐𝒈 𝟐 𝒙 ÷ 𝒚 = 𝒂 − 𝒃
Addition 𝒍𝒐𝒈 𝟐 𝒙 + 𝒚 = 𝒃 + 𝒍𝒐𝒈 𝟐(𝟐 𝒂−𝒃 + 𝟏)
Subtraction 𝒍𝒐𝒈 𝟐 𝒙 − 𝒚 = 𝒃 + 𝒍𝒐𝒈 𝟐(𝟐 𝒂−𝒃 − 𝟏)
a= 𝒍𝒐𝒈 𝟐 𝒙 , b= 𝒍𝒐𝒈 𝟐 𝒚
No existing research addressed it in the image compression domain
Recently: Logarithmic number system (LNS)

Application : Smart-EEG Project (New tool)Application : Smart-EEG Project (New tool)
Mentoring RequirementsMentoring Requirements
 Fast myoclonus jerks
 high frame rate → 100 f/s
• Currently: 30 f/s
Why 100 f/s ?Why 100 f/s ?
 Correct diagnosis
 Real time constraints
Exam procedureExam procedure
EEG acquisition
Video acquisition
Video compression
Sync. + Transmission
Camera
(Video acquisition)
EEG Cap
(acquisition)
Academic
Industry
Hospitals

Compression Block on Smart-EEGCompression Block on Smart-EEG
 HENUC Encoder unit→ implemented in LIP6 by:
 Yhui / Zahid / Laurent
 DWT unit → required for integration → full compression chain
 Many DWT solutions
• SW : GPU/DSP
• HW: ASIC/FPGA
 High speed
 Limitations
 DDR RAM latency not addressed
 The lack of memory optimization and compatibility with HENUC
DWT Related work
Compression algorithm choice: WAAVES

Problem StatementProblem Statement
Does the logarithmic representation has the ability to improve
the trade-off between the compression ratio and the image quality?
Q.1
How to provide a new DWT hardware architecture that can
fulfill the Smart-EEG high-speed requirement?
Q.2

Part III
LNS Library For Image CompressionLNS Library For Image Compression

ObjectivesObjectives
The need of a tool to study the logarithmic domain
 Image compression compatibility
IssuesIssues
 The logarithm of a negative number is undefined
 The logarithm of zero is undefined log(0) = -∞
 The quantization process

Sign AmbiguitySign Ambiguity
Logarithmic
domain
Linear
domain
𝒙= -16𝒙= -16 𝒙 = 16
𝒗 = 𝒍𝒐𝒈 𝟐( 𝒙 )
𝒗 = 𝟒
𝒙 = 𝟐 𝒗
𝒙 = 𝟏𝟔
Linear
domain
Logarithmic
domain
Linear
domain
𝒙= -16𝒙= -16 𝒙 = 16
𝒗 = 𝒍𝒐𝒈 𝟐( 𝒙 )
𝒙 = −𝟏 𝒔
× 𝟐 𝒗
Linear
domain
𝒔 = 𝟏 𝒔 = 𝟎
𝟎 4
𝒔 𝒗
𝟏 4
𝒔 𝒗
𝒙= -16𝒙= -16 𝒙 = 16
Proposed Solution: Sign flag

The logarithm of ZeroThe logarithm of Zero
The importance of ZerosThe importance of Zeros
 Image compatibility
 Efficient coding
 Better compression ratio
Linear
domain
Logarithmic
domain
Linear
domain
𝒙 = 𝟎𝒙 = 𝟎 Ex. L = 0 * yEx. L = 0 * y
𝒗 = 𝟎𝒗 = 𝟎
𝒙 = 𝟎𝒙 = 𝟎 𝑳 = 𝟎𝑳 = 𝟎
Proposed solution: Virtual Zero
𝒍𝒐𝒈 𝟎 = −∞

Logarithmic Quantization : LNS-QLogarithmic Quantization : LNS-Q
LNS-Q Features
Novel quantization method → scaling
Controlled Precision → 𝒏𝒇
 Limited quality degradation
 Smaller quantization error
𝑿 𝑳𝑵𝑺−𝑸 = 𝒓𝒐𝒖𝒏𝒅 𝒙 × 𝑺𝑪
𝑺𝑪 = 𝟏𝟎 𝒏𝒇 = 𝟏, 𝟏𝟎, 𝟏𝟎𝟎, 𝒆𝒕𝒄 , 𝒏𝒇 ≥ 𝟎
𝒙 : un-quantized logarithmic value
𝑿 𝑳𝑵𝑺−𝑸 : quantized logarithmic value
𝑺𝑪 ∶ scaling factor
𝒏𝒇 ∶ number of the fractional digits
LNS-Q
Limitation
× Quality degradation
× Large quantization error
Linear-Q
𝑿 𝒒 = 𝒓𝒐𝒖𝒏𝒅
𝒙
𝒒 𝒔𝒕𝒆𝒑
𝒒 𝒔𝒕𝒆𝒑 ≥ 𝟎 : quantization step
𝒙 : un-quantized value
𝑿 𝒒 : quantized value

LNS Library StructureLNS Library Structure
LNS
Library
Data
LNS-Object
𝑳 = {𝒔, 𝒗}
Sign-flag
𝑳. 𝒔
𝑳. 𝒔 =
𝟎, 𝒙 ≥ 𝟎
𝟏, 𝒙 < 𝟎
Value
𝑳. 𝒗
𝑳. 𝒗 =
𝒍𝒐𝒈( 𝒙 ), 𝒙 ≠ 𝟎
𝟎, 𝒙 = 𝟎
Operators
ADD/SUB
DIV/MUL
𝒙: linear domain

LNS Arithmetic Operators : Multiplication/DivisionLNS Arithmetic Operators : Multiplication/Division
LNS
Operator
A{v,s}A{v,s} B{v,s}B{v,s}
C{v,s}C{v,s}
𝐶. 𝑣 =
0, 𝐴. 𝑣 = 0 𝑜𝑟 𝐵. 𝑣 = 0
𝐴. 𝑣 + 𝐵. 𝑣, 𝑚𝑢𝑙
𝐴. 𝑣 − 𝐵. 𝑣, 𝑑𝑖𝑣
𝐶. 𝑠 =
0, 𝐴. 𝑣 = 0 𝑜𝑟 𝐵. 𝑣 = 0
0, 𝐴. 𝑠 = 𝐵. 𝑠
1, 𝐴. 𝑠 ≠ 𝐵. 𝑠
Multiplication/DivisionMultiplication/Division

LNS Arithmetic Operators : Addition/SubtractionLNS Arithmetic Operators : Addition/Subtraction
LNS
Operator
A{v,s}A{v,s} B{v,s}B{v,s}
C{v,s}C{v,s}
𝐶. 𝑣 =
𝐴. 𝑣 + 𝑓_𝑎𝑑𝑑, 𝐴. 𝑠 = 𝐵. 𝑠
𝐴. 𝑣 + 𝑓_𝑠𝑢𝑏, 𝐴. 𝑠 ≠ 𝐵. 𝑠
𝐴. 𝑣, 𝐵. 𝑣 = 0
𝐵. 𝑣, 𝐴. 𝑣 = 0
0, 𝐴. 𝑣 = 𝐵. 𝑣
0, 𝐴. 𝑣 = 𝐵. 𝑣 = 0
𝐶. 𝑠 =
𝐴. 𝑠, 𝐴 ≥ 𝐵
𝐵. 𝑠, 𝐴 < 𝐵
𝑓_𝑎𝑑𝑑 = log 1 + 2 𝐵.𝑣−𝐴.𝑣 𝑤ℎ𝑒𝑟𝑒 𝐵. 𝑣 > 𝐴. 𝑣
𝑓_𝑠𝑢𝑏 = log 1 − 2 𝐵.𝑣−𝐴.𝑣 𝑤ℎ𝑒𝑟𝑒 𝐵. 𝑣 > 𝐴. 𝑣
Addition/subtractionAddition/subtraction

LNS–Library Validation MethodologyLNS–Library Validation Methodology
X
Y
LNS
Operator
(+,-,,×)
Linear
Operator
(+,-,,×)
LOG
LOG
EXP
Difference
(error)
Reference golden value
Linear domain Linear domainLogarithmic domain

LNS–Library Validation : MAC Case StudyLNS–Library Validation : MAC Case Study
Multiply and Accumulate (MAC) operation
𝑀 =
𝑖=0
𝑛
𝑎 × 𝑖
𝜖 = 𝑀𝑙𝑛𝑠 − 𝑀𝑙𝑖𝑛
Error between logarithmic / linear
𝑎 : constant
𝑛 : number of iterations
𝑀𝑙𝑛𝑠 : MAC output (logarithmic)
𝑀𝑙𝑖𝑛 : MAC output (linear)

LNS Library Validation : 2D LNS-DWT ImplementationLNS Library Validation : 2D LNS-DWT Implementation
DWT-based 9/7 CDF filter
o JPEG2000/WAAVES
Lifting Scheme
o More efficient than the convolution approach
o Less memory requirements
Validation results
o Absolute error:
• between linear/logarithmic around 7×10−10
1D LNS-DWT
(rows)
1D LNS-DWT
(rows)
Horizontal Transform
1D LNS-DWT
(columns)
1D LNS-DWT
(columns)
Vertical Transform
LOGLOG
Input image DWT coefficients

LNS-Q ValidationLNS-Q Validation
DWTcoefficientvalue
DWT coefficient location
 Small Quantization Error

SummarySummary
• MAC → 7×10−8 (1000 iterations)
• LNS-DWT → 7×10−10
• DWT+LNS-Q
Novel LNS-LibraryNovel LNS-Library
 Image compression compatibility
 Virtual zero
 Sign flag
 Novel logarithmic-based Quantization method (LNS-Q)
o Scaling-based
ValidationValidation

PART IV
Logarithmic DWT based CompressionLogarithmic DWT based Compression

LNS-DWT/LNS-Q Integration with WAAVESLNS-DWT/LNS-Q Integration with WAAVES
EncoderOriginal
Image LNS-Q
LNS
DWT
Compression Side
Encoder
Compressed
Image
.COD
LOG
LimitationsLimitations Limited range of compression ratio .. Why ?

LNS Vs Linear DWT Dynamic RangeLNS Vs Linear DWT Dynamic Range
LNS
Better quality
Linear
Higher compression ratio

LNS Vs Linear DWT Data DistributionLNS Vs Linear DWT Data Distribution
Q: How to combines the advantages of the both domains into a single bit-stream ?
LNS Linear

Hybrid-DWTHybrid-DWT
LL HL
LH HH
LNS Zeros
Zeros Zeros
Zeros Linear
Linear Linear
LNS FLP
FLP FLP
Linear DWT
LL HL
LH HH
LNS DWT Masked LNS DWT
Masked Linear DWT
Merged DWT
LNS/Linear
Stage 1 Stage 2 Stage 3DescriptionDescription
 DWT coefficients → 2 parts
• LL sub-band → Logarithmic
• The rest sub-bands → Linear
 New compression parameter:
• NL : number of linear levels
• Trade-off between
o Compression ratio
o Image quality

LNS-DWT Dynamic Range Reduction FilterLNS-DWT Dynamic Range Reduction Filter
IssueIssue
 Small values in the linear domain → large negative values in the
logarithmic domain
 That affects the encoding efficiency
ObjectiveObjective
 To Increase the number of zeros → improve the coding efficiency
HowHow
 Threshold (FTH) is used to choose which value are removed
 Replace the very large negative values with zeros in LNS-DWT
Part of DWT coefficients before quantizationPart of DWT coefficients before quantization
After quantization onlyAfter quantization only
After DRRAfter DRR

LNS-WAAVES based on Hybrid-DWTLNS-WAAVES based on Hybrid-DWT
NL
B
FTH
SC
• B : Logarithmic base
• NL : Number of linear DWT level
• FTH : DRR threshold
• q : Quantization step (linear)
• SC : LNS-Q scale factor
q
Input
Image
Hybrid
DWT
Encoder
(HENUC)
Compressed
Image
LOG
DRR
Filter
Quantization
LNS-Q
Linear-Q

Evaluation MethodologyEvaluation Methodology
 Experiments outlines:
 Log base effect
 NL effect
 DRR effect
 Quantization effect
 Experiments outlines:
 Log base effect
 NL effect
 DRR effect
 Quantization effect
Image

Image Quality Assessment : PSNR or SSIM ?Image Quality Assessment : PSNR or SSIM ?
𝑷𝑺𝑵𝑹 𝒅𝑩 =
𝟐𝟎 𝒍𝒐𝒈 𝟏𝟎(𝒎𝒂𝒙𝒊𝒎𝒖𝒎 𝒑𝒊𝒙𝒆𝒍 𝒗𝒂𝒍𝒖𝒆)
𝑴𝑺𝑬
𝑺𝑺𝑰𝑴 𝒇, 𝒈 =
𝟐𝝁 𝒇 𝝁 𝒈 + 𝑪 𝟏 + 𝟐𝝈 𝒇 𝝈 𝒈 + 𝑪 𝟐
(𝝁 𝒇
𝟐
𝝁 𝒈
𝟐
+ 𝑪 𝟏)(𝝈 𝒇
𝟐
𝝈 𝒈
𝟐
+ 𝑪 𝟐)
SSIM measures the image quality in terms of:
• Structural
• Luminance
• Contrast
PSNR depends only on the mean square error (MSE):
𝝁 𝒇 , 𝝁 𝒈 Mean intensity for images f , g
𝑪 𝟏 , 𝑪 𝟐 Constants
𝝈 𝒇 , 𝝈 𝒈 Standard deviation for images f , g
Assume an original image and a reconstructed image, f and g respectively

The change-of-base formula
Results : The Log Base EffectResults : The Log Base Effect
 Yields a smaller logarithmic value
 Less dynamic range
 Better compression ratio
 Less quality
𝑙𝑜𝑔 𝑏 𝑥 =
𝑙𝑜𝑔 𝑘(𝑥)
𝑙𝑜𝑔 𝑘(𝑏)
The higher base of a logarithm (B)

Results : The impact of LNS-Q and NLResults : The impact of LNS-Q and NL
NL = 1 → Max CR = 18 NL = 2 → Max CR = 60 NL = 3 → Max CR = 140
NL: number of linear sub-bands

Results : The Influence of the QuantizationResults : The Influence of the Quantization
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SSIM improvement (QUALITY)
 Better than JPEG2000 by:
 8% to 55% → at SC = 100
 5% to 44% → at SC = 10
 3% to 22% → at SC = 1
 Better than WAAVES by:
 7% to 44% → at SC = 100
 4% to 38% → at SC = 10
 2% to 10% → at SC = 1
LNS-DWT Mohammed IBRAHEEM – LIP6-UMPC-CIRA

Results : The Impact of the DRRResults : The Impact of the DRR
 DRR: dynamic range reduction filter

SummarySummary
LNS-WAAVES : novel compression schemeLNS-WAAVES : novel compression scheme
Hybrid-DWTHybrid-DWT
Merging DWT coefficients in a hybrid fashion = linear + logarithmic domains
 Based on Hybrid-DWT/LNS-Q
1. Log base effect
• B= 2 give the best quality due to less quantization error
2. NL effect
• NL = 3 gives the best compression range
3. Quality Improvement:
• of 8% up to 34% compared to WAAVES

Part V
2D-DWT Hardware Architecture2D-DWT Hardware Architecture

The second research question & Motivation
• Compression SPEED on embedded systems
• Smart EEG requirements
• The need of a high-speed DWT for a video compression (100 fps)
 Which DWT Algorithm suitable for hardware (Lifting /convolution) ?
• Lifting is more efficient:
• Less operations
• Less memory requirements (in-place computation)
• Less memory access

DWT Algorithm IssuesDWT Algorithm Issues
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 Data dependency
 1D-DWT for each row, THEN
 1D-DWT for each column
 Memory access
 Horizontal transform
• Read the input image
• Write the output coefficients
 Vertical transform
• Read the horizontal coefficients
• Write the output vertical coefficients
Input imageInput image
LowLowHighHigh
LowLow HighHighLowLow HighHigh

Lifting scheme AnalysisLifting scheme Analysis
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Split input data vector
Even/Odd
Stage: Predict 1
P1 = current even pix + α(pix previous + pix next)
Stage: Update 1
U1 = current odd pixel + β (U1 previous + U1 next)
Stage: Predict 2
P2 = current P1 + γ (U1 previous + U1 next)
Stage : Update 2
U2 = current U1 + δ (P2 previous + P2 next)
Stage: Scaling P2
Stage: Scaling U2
The Lifting DWT algorithm
Issues
• Each stage depends on the previous one
o Parallelism complexity
• For the 2D transform
o The need to wait the row to processed before
starting processing the columns.
 Solution
 To achieve high parallelism
 Efficient memory organization
 Partial DWT computation of the image
o Process few rows then,
o Start process the columns
 The even/odd data in the columns
can be processed independently

4-Port Memory and External memory interface4-Port Memory and External memory interface
phase-locked loop

Horizontal / Vertical 1D DWTHorizontal / Vertical 1D DWT
 Simple computation units
 Short critical path (adder +multiplier)
 8 pixels in parallel (4 odd + 4 even)
 Parallel horizontal/ vertical transform

Proposed Unified 2D DWT ArchitectureProposed Unified 2D DWT Architecture
FeaturesFeatures
Line BuffersLine Buffers
 [Even/Odd] pixels split on-the-fly
 Novel LB scheme two features
• 4-port memories → parallel operation
 Data concatenation
• 4 pixels/location
• 4 odd pixels parallel
• 4 even pixels parallel
 High throughput
 Parallel Horizontal/Vertical transform
 Novel custom memories
 Scalability

Results : Resources on DE4 FPGA boardResults : Resources on DE4 FPGA board
Altera Stratix IV GX230 resources utilization for 1080p

Results : Architecture ScalabilityResults : Architecture Scalability
a) FPGA prototyping results including DMAs latency
b) F_Exp: Experimental frequency in MHz
c) Maximum core logic frequency in MHz

Results : Comparison with Existing WorksResults : Comparison with Existing Works
Aziz et al.
2012
FPGA
Sameeen et al.
2012
FPGA
Hu et al.
2013
ASIC
Hsia et al.
2013
ASIC
Darji et al.
2014
ASIC
Darji et al.
2014
FPGA
This work
Cycles/pixel 1 1.55 0.5 0.75 0.5 0.5 0.125
Frame/s 53 24 n/a n/a n/a n/a 120
DWT filter 5/3 9/7 & 5/3 9/7 9/7 & 5/3 9/7 9/7 & 5/3 9/7
Sys. Freq 221.44 133.3 50 100 100 100 125
DRR Freq n/a 266 n/a n/a n/a n/a 250
Bit/pixel 8-bit 32-bit 8-bit 16-bit n/a n/a 32-bit
Add/Mul 2/0 n/a 116/188 16/0 16/10 16/10 68/54
Critical Path 2 adders n/a Mul + add 2 Mul+ 4 Add mul Mul + add Mul + add
Scalability No No Yes No No No Yes
Frame size 512×512 1920×1080 512×512 256×256 256×256 1920×1080 1920×1080

SummarySummary
 A unified 2D DWT computation architecture
• Horizontal/Vertical transform simultaneously
 4-Port Line buffers
• Eliminate the inefficient reading or writing columns of an image from/to DDR
RAM
• Parallel read/write from the external RAM
• Parallel transform
• Memory size optimization by having less temporary buffers (in-place calculation)
 Throughput :
• 120 fps 1080p
 Scalable architecture
• Support high resolution images up to 4K

Part VI
Conclusion and Future workConclusion and Future work

An LNS library as ToolAn LNS library as Tool
The virtual zero → efficient encoding
The sign flag → solved the sign ambiguity problem
Novel quantization method LNS-Q
• Scaling operation
• Limited quantization error
Library validation → small Error compared to the FLP ≈ 𝟕 × 𝟏𝟎−𝟕
Hybrid-DWT: Sub-bands → Two parts: logarithmic + linear
Advantages
 Enhanced the image quality
 better compression ratio
LNS-WAAVESLNS-WAAVES
ConclusionConclusion
LNS-WAAVES has Improvement in the quality:
 8% up to 34% better than WAAVES
 10% up to 49% better than JPEG2000

ConclusionConclusion
 A high throughput of 8 pixels/clock cycle
 Processing speed up to 120 fps Full-HD
Novel DWT ArchitectureNovel DWT Architecture
Key FeaturesKey Features
A unified 2D DWT computation
 parallel Horizontal/Vertical transform
4-port line buffers → parallel process :
 DMA reading/writing
 Horizontal/vertical
 A 2x reduction in the required DDR RAM bandwidth
 Scalable architecture

Future workFuture work
Image compression based logarithmic arithmetic is a promising research area
Exploring the WAAVES HENUC encoder
• How to switch the encoding algorithm into the logarithmic domain
• Scan/sort
• To be adapted with the logarithmic DWT coefficients
Building a logarithmic computation unit and integrating it with proposed architecture
• support the hybrid-dwt
Lossless compression mode by including the DWT LeGall 5/3
Logarithmic compressionLogarithmic compression
Embedded SystemsEmbedded Systems

List of Publications : 2 International JournalsList of Publications : 2 International Journals
 L. Lambert, J. Despatin, I. Dhif, I. Mhedhbi, M. Shaaban Ibraheem, A. Syed-Zahid, B. Granado, K. Hachicha, A.
Pinna, P. Garda, F. Kaddouh, M. Terosiet, A. Histace, O. Romain, C. Bellet, F. Durand, J.P. Commes, S. Hochberg, D.
Heudes, P. Lozeron,and N. Kubis. “Telemedecine, electroencephalography and current issues. smart-eeg: An
innovative solution.” European Research in Telemedicine, 4(3):81 – 86, 2015.
 Mohammed Shaaban Ibraheem, Khalil Hachicha, Syed Zahid Ahmed, Laurent Lambert, and Patrick Garda. “A
scalable high throughput 2d dwt architecture for a medical application”. Journal of Real-Time Image Processing,
submitted: Jan 2017. (under peer-review )

List of Publications : 4 International ConferencesList of Publications : 4 International Conferences
 Mohammed Shaaban Ibraheem, Syed Zahid Ahmed, Khalil Hachicha, Sylvain Hochberg, and Patrick Garda:
“A low ddr bandwidth 100fps 1080p video 2d discrete wavelet transform implementation on fpga”. In
Proceedings of the 2016 ACM/SIGDA International Symposium on Field-Programmable Gate Arrays, FPGA
’16, pages 274–274, New York, NY, USA, 2016. ACM.
 M. S. Ibraheem, S. Z. Ahmed, K. Hachicha, S. Hochberg, and P. Garda. “Medical images compression with
clinical diagnostic quality using logarithmic dwt.” In 2016 IEEE-EMBS International Conference on
Biomedical and Health Informatics (BHI), pages 402–405, Feb 2016.
 Mohammed IBRAHEEM, Khalil Hachicha, Syed Ahmed, Sylvain Hochberg, and Patrick Garda.
“Logarithmic discrete wavelet transform for medical image compression with diagnostic quality.” In
Proceedings of the 5th EAI International Conference on Wireless Mobile Communication and Healthcare,
MOBIHEALTH’15, pages 272–275, ICST, Brussels, Belgium, Belgium, 2015. ICST (Institute for Computer
Sciences, Social- Informatics and Telecommunications Engineering).
 Dhif, M. S. Ibraheem, L. Lambert, K. Hachicha, A. Pinna, S. Hochberg, I. Mhedhbi, and P. Garda. “A novel
approach using waaves coder for the eeg signal compression”. In 2016 IEEE-EMBS International Conference
on Biomedical and Health Informatics (BHI), pages 453–456, Feb 2016.

List of Publications : 5 National WorkshopsList of Publications : 5 National Workshops
 M. Shaaban Ibraheem, Khalil Hachicha, Imen Mhedbi, Sylvain Hochberg, Patrick Garda, S. Zahid Ahmed. “Logarithmic-
based dwt for medical images compression”. In Colloque de la Fédération d’Électronique, Thème : Internet des objets pour
les applications biomédicales, Issy-les-Moulineaux, France, 2016.
 M. Shaaban Ibraheem, Sylvain Hochberg, Patrick Garda, Syed Zahid Ahmed. “Study of applying logarithmic dwt for
medical images compression”. In 11ème Colloque du GDR SoC-SiP, Nantes, France, 2016.
 L. Lambert, S. Z. Ahmed B. Granado K. Hachicha A. Pinna, M. S. Ibraheem I. Dhif and P.Garda. “Smart-eeg, a new
platform for tele-expertise of electroencephalogram.” In 11ème Colloque du GDR SoC-SiP, Nantes, France, 2016.
 Dhif, I. Mhedhbi, M. Shaaban Ibraheem, A. Syed-Zahid, B.Granado, K. Hachicha, A. Pinna, P. Garda, F. Kaddouh, M.
Terosiet, A. Histace, O.Romain, C. Bellet, F. Durand, J.P. Commes, S. Hochberg, D. Heudes, P. Lozeron, N.Kubis, L.
Lambert, J. Despatin. “Telemedecine, electroencephalography and current issues smart-eeg: An innovative solution.” In
8ème édition du Congrès SFT ANTEL, Centre Universitaire des Saints Pères, Paris, 2015.
 L. Lambert, M. Shaaban Ibraheem, S. Zahid Ahmed, B. Granado, K. Hachicha, A. Pinna, P. Garda,, I. Dhif, “Smart-eeg :
A new platform for tele-expertise of electroencephalogram” In GDR SOC SIP, Paris, 2014.

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Logarithmic Discrete Wavelet Transform for High-Quality Medical Image Compression

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Logarithmic Discrete Wavelet Transform for High-Quality Medical Image Compression